STUDENT TEXT AND HOMEWORK HELPER

UNIT 4 EXPONENTIAL FUNCTIONS AND EQUATIONS STUDENT TEXT AND HOMEWORK HELPER Randall I. Charles Allan E. Bellman Basia Hall William G. Handlin, Sr. Dan Kenned Stuart J. Murph Grant Wiggins Boston, Massachusetts Chandler, Arizona Glenview, Illinois Hoboken, New Jerse

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UNIT 4 EXPONENTIAL FUNCTIONS AND EQUATIONS TOPIC 9 Eponential Functions and Equations TOPIC 9 Overview...384 9-1 Eponential Functions...386 9- Eponential Growth and Deca...395 9-3 Modeling Eponential Data...40 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS (TEKS) FOCUS (9)(A) (9)(B) (9)(C) Determine the domain and range of eponential functions of the form f () = ab and represent the domain and range using inequalities. Interpret the meaning of the values of a and b in eponential functions of the form f () = ab in real-world problems. Write eponential functions in the form f () = ab (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and deca. (9)(D) Graph eponential functions that model growth and deca and identif ke features, including -intercept and asmptote, in mathematical and real-world problems. (9)(E) Write, using technolog, eponential functions that provide a reasonable fit to data and make predictions for real-world problems. (1)(B) Evaluate functions, epressed in function notation, given one or more elements in their domains. Contents

Topic 9 Eponential Functions and Equations TOPIC OVERVIEW VOCABULARY 9-1 Eponential Functions 9- Eponential Growth and Deca 9-3 Modeling Eponential Data English/Spanish Vocabular Audio Online: English Spanish asmptote, p. 386 asíntota compound interest, p. 396 interés compuesto deca factor, p. 396 factor de decremento eponential deca, p. 396 decremento eponencial eponential function, p. 386 función eponencial eponential growth, p. 395 incremento eponencial growth factor, p. 395 factor incremental DIGITAL APPS PRINT and ebook Access Your Homework... ONLINE HOMEWORK You can do all of our homework online with built-in eamples and Show Me How support! When ou log in to our account, ou ll see the homework our teacher has assigned ou. YOUR DIGITAL RESOURCES PearsonTEXAS.com HOMEWORK TUTOR APP Do our homework anwhere! You can access the Practice and Application Eercises, as well as Virtual Nerd tutorials, with this Homework Tutor app, available on an mobile device. 384 Topic 9 Eponential Functions and Equations STUDENT TEXT AND HOMEWORK HELPER Access the Practice and Application Eercises that ou are assigned for homework in the Student Tet and Homework Helper, which is also available as an electronic book.

Big Time Pa Back 3-Act Math 3-Act Math Most people agree that investing our mone is a good idea. Some people might advise ou to put mone into a bank savings account. Other people might sa that ou should invest in the stock market. Still others think that buing bonds is the best investment option. Is a bank savings account a good wa to let our mone grow? Just how much mone can ou make from a savings account? In this video, ou ll see an intriguing situation about an investment option. Scan page to see a video for this 3-Act Math Task. If You Need Help... VOCABULARY ONLINE You ll find definitions of math terms in both English and Spanish. All of the terms have audio support. INTERACTIVE EXPLORATION You ll have access to a robust assortment of interactive eplorations, including interactive concept eplorations, dnamic activitites, and topiclevel eploration activities. LEARNING ANIMATIONS You can also access all of the stepped-out learning animations that ou studied in class. STUDENT COMPANION Refer to our notes and solutions in our Student Companion. Remember that our Student Companion is also available as an ACTIVebook accessible on an digital device. INTERACTIVE MATH TOOLS These interactive math tools give ou opportunities to eplore in greater depth ke concepts to help build understanding. VIRTUAL NERD Not sure how to do some of the practice eercises? Check out the Virtual Nerd videos for stepped-out, multi-level instructional support. PearsonTEXAS.com 385

9-1 Eponential Functions TEKS FOCUS TEKS (9)(A) Determine the domain and range of eponential functions of the form f() = ab and represent the domain and range using inequalities. TEKS (1)(C) Select tools, including real objects, manipulatives, paper and pencil, and technolog as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. Additional TEKS (1)(A), (1)(D), (9)(C), (9)(D), (1)(B) VOCABULARY Asmptote An asmptote is a line that a graph of a function gets closer to as or gets larger in absolute value. Eponential function An eponential function is a function of the form = ab, where a is a nonzero constant, b 7 0, and b 1. Number sense the understanding of what numbers mean and how the are related ESSENTIAL UNDERSTANDING Some functions model an initial amount that is repeatedl multiplied b the same positive number. In the rules for these functions, the independent variable is an eponent. Definition An eponential function is a function of the form = a # b, where a 0, b 7 0, b 1, and is a real number. Eamples Ke Concept Eponential Function 4 4 O 4 4 4 4 O 4 1 4 1 386 Lesson 9-1 Eponential Functions

Ke Concept Asmptote of an Eponential Function = ab The -ais ( = 0) is the horizontal asmptote for an eponential function of the form = ab. The -values approach zero, but never actuall reach zero. The graphs approach, but do not cross, the -ais. O The -ais is an asmptote. Problem 1 Identifing Linear and Eponential Functions How can ou identif a constant ratio between -values? When ou multipl each -value b the same constant and get the net -value, there is a constant ratio between the values. Does the table or rule represent a linear or an eponential function? Eplain. A 0 1 1 3 The difference between the -values is 1. 9 3 7 0 1 + 1 * 3 1 3 + 1 * 3 9 + 1 * 3 3 7 The ratio between the -values is 3. The table represents an eponential function. There is a common difference between consecutive -values and a common ratio between the corresponding -values. B = 3 The rule represents a linear function because it is in the form = m + b. The independent variable is not an eponent. PearsonTEXAS.com 387

Problem TEKS Process Standard (1)(C) Writing an Eponential Function The figures below are stages of the Sierpinski triangle. In Stage 0, there is one black triangle. In each subsequent stage, a white triangle is added to the center of each black triangle, dividing that triangle into 3 black triangles and 1 white triangle. The number of black triangles increases b a factor of 3 in each stage. Stage 0 Stage 1 Stage Stage 3 Stage 4 Is there an stage with eactl 1000 black triangles? No. At each stage the number of black triangles will be a multiple of 3. A Write an eponential function f () = ab to describe this situation. The factor b which the number of black triangles increases at each stage is the value of b. Using the fact that b is 3, ou can show that the value of a is 1, the number of triangles in Stage 0. f () = ab Write the formula for the eponential function. f () = a # 3 Substitute 3 for b. 1 = a # 3 0 From Stage 0, ou know that f(0) = 1. 1 = a # 1 Simplif 3 0. 1 = a Solve for a. f () = 1 # 3 Substitute 1 for a in the formula f() = a # 3. f () = 3 Simplif. B Determine in what stage there will first be more than 1000 black triangles. You can select techniques such as estimation and mental math to solve this problem. In Stage, ou know there are 9 black triangles. Round 9 to 10 and then multipl b the factor 3 to estimate the number of black triangles in later stages. The estimate of 900 in Stage 6 is high, since ou rounded up in earlier stages. So, ou know the number of black triangles in Stage 6 is less than 1000. When ou multipl b 3 again, the number of black triangles will eceed 1000. There will first be more than 1000 black triangles in Stage 7. Check You can confirm this result b evaluating f (6) and f (7). f () = 3 6 = 79 f () = 3 7 = 187 Stage 3 4 5 6 Triangle Estimate 10 30 30 3 = 90 Now round 100 90 to 100. 300 900 388 Lesson 9-1 Eponential Functions

Problem 3 TEKS Process Standard (1)(A) Evaluating an Eponential Function Wh is the function 30 ~ not ~ 30? In an eponential function, a is the starting value and b is the common ratio. Population Growth Suppose 30 flour beetles are left undisturbed in a warehouse bin. The beetle population doubles each week. The function f () = 30 # gives the population after weeks. How man beetles will there be after 56 das? f () = 30 # = 30 # 8 56 das is equal to 8 weeks. Evaluate the function for = 8. = 30 # 56 Simplif the power. = 7680 Simplif. After 56 das, there will be 7680 beetles. Problem 4 TEKS Process Standard (1)(D) How can ou use the graph to find the domain and range? The domain can be found b using the -coordinates on the graph and the range can be found b using the -coordinates on the graph. Graphing an Eponential Function A What is the graph of = 3 ~? Identif the domain and range. Epress the range using an inequalit. Make a table of - and -values. 1 3 (, ) 3 3 3 4, 3 4 3 1 3 1 1 1 1, 1 1 0 3 0 3 1 3 (0, 3) 1 3 1 3 6 (1, 6) 10 8 6 4 Plot the points. 3 3 4 1 (, 1) An value substituted for results in a positive -value. The domain is all real numbers. The range is 7 0. O 4 B What is the -intercept of the eponential function in part (A)? What is the asmptote? The table and the graph show that when = 0, = 3. The -intercept of = 3 # is 3. The table and the graph show that as decreases, the -values get smaller. The value of 3 # will alwas be positive, so the -values will approach zero, but never reach zero. The -ais is the horizontal asmptote for = 3 #. Connect the points with a smooth curve. PearsonTEXAS.com 389

Problem 5 Graphing an Eponential Model Maps Computer mapping software allows ou to zoom in on an area to view it in more detail. The function f() = 100 ~ 0.5 models the percent of the original area the map shows after zooming in times. Graph the function. Identif the -intercept, the asmptote, and the domain. ORIGINAL AREA 75 Big Cpress National Preserve 41 Loahatchee NWR 7 Miami Everglades National Park Homestead 1 95 Boca Raton Fort Lauderdale ATLANTIC OCEAN W N E S 0 0 mi 0 1 3 4 f() 100 0.5 (, f()) 100 0.5 0 100 (0, 100) 100 0.5 1 5 (1, 5) 100 0.5 6.5 (, 6.5) 100 0.5 3 1.56 (3, 1.56) 100 0.5 4 0.39 (4, 0.39) ZOOMED IN 1 TIME 41 75 7 81 Everglades National Park Homestead 5 1 Miami Fort Lauderdale 95 Hollwood Biscane Ba ATLANTIC OCEAN W N E S 0 10 mi Should ou connect the points of the graph? No, the data is discrete not continuous. The number of times ou zoom in must be a nonnegative integer. 100 80 60 40 0 O f() 4 41 ZOOMED IN TIMES 5 75 81 7 1 81 86 Pinecrest 81 Hialeah 11 95 Miami Biscane Ba Aventura 1 195 ATLANTIC OCEAN W N E S 0 5 mi When = 0, = 100, so the -intercept is 100. The -ais is the horizontal asmptote. The domain is Ú 0, is an integer. Problem 6 TEKS Process Standard (1)(C) Solving One-Variable Equations What is the solution or solutions of = 0.5 +? Step 1 Write each side of the equation as a function equation. f () = and g () = 0.5 + Step Graph the equations using a graphing calculator. Use 1 for f () and for g (). continued on net page 390 Lesson 9-1 Eponential Functions

Problem 6 continued How can ou check that the -value is a solution? Substitute for in the original equation. Make sure ou use the same -value for each instance of. Step 3 Use the CALC feature. Chose INTERSECT to find the points where the lines intersect. Intersection 3.865.06874981 The solutions of = 0.5 + are about -3.86 and 1.44. Intersection 1.4449076.74538 ONLINE H O M E W O R K PRACTICE and APPLICATION EXERCISES Scan page for a Virtual Nerd tutorial video. Determine whether each table or rule represents a linear or an eponential function. Eplain wh or wh not. For additional support when completing our homework, go to PearsonTEXAS.com. 1. 1 3 4. 8 3 18 0 6 1 9 1 3 15 3. = 4 # 5 4. = 1 # 5. =-5 # 0.5 6. = 7 + 3 Evaluate each function for the given value. 7. f () = 6 for = 8. g(t) = # 0.4 t for t =- 9. = 0 # 0.5 for = 3 10. h(w) =-0.5 # 4 w for w = 18 11. Appl Mathematics (1)(A) An investment of $5000 doubles in value ever decade. The function f () = 5000 #, where is the number of decades, models the growth of the value of the investment. How much is the investment worth after 30 r? 1. Appl Mathematics (1)(A) A population of 75 foes in a wildlife preserve quadruples in size ever 15 r. The function = 75 # 4, where is the number of 15-r periods, models the population growth. How man foes will there be after 45 r? Graph each eponential function. Identif the domain, range, -intercept, and asmptote of each function. Epress each range using an inequalit. 13. = 4 14. =-4 15. = ( 1 3 ) 16. =-( 1 3 ) 17. = 10 # ( 3 ) 18. = 0.1 # 19. = 1 4 # 0. = 1.5 Select Tools to Solve Problems (1)(C) Use a graph to solve each equation. 1. 4 = 3 + 5. + 3 = 3 PearsonTEXAS.com 391

3. Analze Mathematical Relationships (1)(F) A new museum had 7500 visitors this ear. The museum curators epect the number of visitors to grow b 5% each ear. The function = 7500 # 1.05 models the predicted number of visitors each ear after ears. Graph the function. Identif the domain, range, -intercept, and asmptote of the function. Epress the range using an inequalit. 4. Use Multiple Representations to Communicate Mathematical Ideas (1)(D) A solid waste disposal plan proposes to reduce the amount of garbage each person throws out b % each ear. This ear, each person threw out an average of 1500 lb of garbage. The function = 1500 # 0.98 models the average amount of garbage each person will throw out each ear after ears. Graph the function. Identif the domain, range, -intercept, and asmptote of the function. Epress the range using an inequalit. 5. Use Multiple Representations to Communicate Mathematical Ideas (1)(D) Compare the rule and the function table below. Which function has the greater value when = 1? Eplain. Function 1 Function = 4 1 5 5 3 4 15 65 6. You have just read a journal article about a population of fungi that doubles ever n 3 weeks. The beginning population was 10. The function = 10 # 3 represents the population after n weeks. a. You have a population of 15 of the same fungi. Assuming the journal article gives the correct rate of increase, write the function that represents the population of fungi after n weeks. b. Suppose ou find another article that states that the fungi population triples ever 4 weeks. If there are currentl 15 fungi in our population, write the function that represents the population after n weeks. 7. Eplain Mathematical Ideas (1)(G) Hdra are small freshwater animals. The can double in number ever two das in a laborator tank. Suppose one tank has an initial population of 60 hdra. When will there be more than 5000 hdra? 8. a. Graph =, = 4, and = 0.5 on the same aes. b. What point is on all three graphs? c. Does the graph of an eponential function intersect the -ais? Eplain. d. How does the graph of = b change as the base b increases or decreases? Hdra 39 Lesson 9-1 Eponential Functions

Write an eponential function to describe the given sequence of numbers. 9., 8, 3, 18, 51,... 30. 1 3, 1 9, 1 7, 1 81,... Which function has the greater value for the given value of? 31. = 4 or = 4 for = 3. f () = 10 # or f () = 00 # for = 7 33. = 3 or = 3 for = 5 34. f () = or f () = 100 for = 10 35. Appl Mathematics (1)(A) A computer valued at $1500 loses 0% of its value each ear. a. Write a function rule that models the value of the computer. b. Find the value of the computer after 3 r. c. In how man ears will the value of the computer be less than $500? 36. a. Graph the functions = and = on the same aes. b. What do ou notice about the graphs for the values of between 1 and 3? c. How do ou think the graph of = 8 would compare to the graphs of = and =? 37. Eplain Mathematical Ideas (1)(G) Find the range of the function f () = 500 # 1 using the domain 51,, 3, 4, 56. Eplain wh the definition of eponential function states that b 1. Evaluate each function over the domain {, 1, 0, 1,, 3}. As the values of the domain increase, do the values of the range increase or decrease? 38. f () = 5 39. =.5 40. h() = 0.1 Solve each equation. 41. = 64 4. 3 = 1 7 43. 3 # = 4 44. 5 # - 15 = 8 45. Suppose (0, 4) and (, 36) are on the graph of an eponential function. a. Use (0, 4) in the general form of an eponential function, = a # b, to find the value of the constant a. b. Use our answer from part (a) and (, 36) to find the value of the constant b. c. Write a rule for the function. d. Evaluate the function for =- and = 4. 46. A population of 150 dandelions is growing in a meadow. A computer model predicts that the population will increase b a factor of 1. ever week. Write an equation to show the population as a function of time, in which is the number of weeks. What will be the approimate population after 4 weeks? PearsonTEXAS.com 393

47. A bank offers a special account in which the accept an initial deposit of 3 cents, and then double the value of the account ever month. a. Write an equation to show the value of the account in dollars as a function of months. What is the value in the account after 3 months? b. Select Techniques to Solve Problems (1)(C) Select a technique such as number sense, mental math, or estimation to determine when the value of the account will be more than $15. TEXAS End-of-Course PRACTICE 48. A population of 30 swans doubles ever 10 r. Which graph represents the population growth? A. C. 10 10 Swans 60 0 0 0 40 Years B. D. 30 Swans 15 Swans Swans 60 0 0 0 40 Years 10 60 0 0 0 40 Years 0 0 0 40 Years 49. Which equation do ou get when ou solve = - 1 for? F. = - 6 H. = 0.5-6 G. = + 6 J. = 0.5 + 6 394 Lesson 9-1 Eponential Functions

9- Eponential Growth and Deca TEKS FOCUS TEKS (9)(B) Interpret the meaning of the values of a and b in eponential functions of the form f () = ab in real-world problems. TEKS (1)(A) Appl mathematics to problems arising in everda life, societ, and the workplace. Additional TEKS (1)(G), (9)(C), (9)(D) VOCABULARY Compound interest interest paid on both the principal and the interest that has alread been paid Deca factor 1 minus the percent rate of change epressed as a decimal for an eponential deca situation; the base b in the function = a # b Eponential deca a situation that can be modeled with a function of the form = a # b, where a 7 0 and 0 6 b 6 1 Eponential growth a situation that can be modeled with a function of the form = a # b, where a 7 0 and b 7 1 Growth factor 1 plus the percent rate of change epressed as a decimal for an eponential growth situation; the base b in the function = a # b Appl use knowledge or information for a specific purpose, such as solving a problem ESSENTIAL UNDERSTANDING An eponential function can model growth or deca of an initial amount. Ke Concept Eponential Growth Definitions Eponential growth can be modeled b the function = a # b, where a 7 0 and b 7 1. The base b is the growth factor, which equals 1 plus the percent rate of change epressed as a decimal. Graph Algebra The initial amount (when 0) is also the -intercept. T a b d eponent c The base, which is greater than 1, is the growth factor. a b b 1 O (0, a) PearsonTEXAS.com 395

Ke Concept Compound Interest When a bank pas interest on both the principal and the interest an account has alread earned, the bank is paing compound interest. You can use the following formula to find the balance of an account that earns compound interest. A = P(1 + n) r nt A = the balance P = the principal (the initial deposit) r = the annual interest rate (epressed as a decimal) n = the number of times interest is compounded per ear t = the time in ears Ke Concept Eponential Deca Definitions Eponential deca can be modeled b the function = a # b, where a 7 0 and 0 6 b 6 1. The base b is the deca factor, which equals 1 minus the percent rate of change epressed as a decimal. Algebra The initial amount (when 0) is also the -intercept. T a b d eponent c The base is the deca factor. Graph O a b 0 b 1 (0, a) Problem 1 Graphing an Eponential Growth Function You are observing a bacteria population in a laborator culture. The population doubles ever 30 min. The function p() = 500 ~ models the population, where is the number of 30-minute periods since ou began observing. Does the point ( 1, 50) have meaning in this situation? =-1 corresponds to the time 30 min before ou start observing the bacteria population. Thirt minutes before ou start, the number of bacteria is 50. A Graph the function p() = 500 ~, identifing the -intercept and asmptote. The equation p() = 500 # is in the form = a # b, where a = 500 and b =. Since b 7 1, the function represents eponential growth. The graph rises from left to right and has a -intercept of 500. The asmptote is the -ais, with the graph approaching the -ais as decreases. B What is the meaning of the -intercept in this situation? The -intercept 500 occurs when is 0, which corresponds to the time ou start observing the population. There are 500 bacteria present when ou start observing. -4-4000 3000 000 1000 O 4 396 Lesson 9- Eponential Growth and Deca

Problem TEKS Process Standard (1)(A) Modeling Eponential Growth Economics Since 005, the amount of mone spent at restaurants in the United States has increased about 7% each ear. In 005, about $360 billion was spent at restaurants. When can ou use an eponential growth function? You can use an eponential growth function when an initial amount increases b a fied percent each time period. A If the trend continues, about how much will be spent at restaurants in 015? Relate = a # b Use an eponential function. Define Let = the number of ears since 005. Let = the annual amount spent at restaurants (in billions of dollars). Let a = the initial amount spent (in billions of dollars), 360. Let b = the growth factor, which is 1 + 0.07 = 1.07. Write = 360 # 1.07 Use the equation to predict the annual spending in 015. = 360 # 1.07 = 360 # 1.07 10 015 is 10 r after 005, so substitute 10 for. 708 Round to the nearest billion dollars. About $708 billion will be spent at restaurants in 015 if the trend continues. B What is an epression that represents the equivalent monthl increase of spending at U.S. restaurants in 005? You will need to find an epression of the form r m, where r is approimatel the monthl growth factor and m is the number of months. You know that 1.07 represents the earl increase where is the number of ears. 1.07 = 1.07 1 1 There are 1 months in ears. = 11.07 1 1 1 Power raised to a power 1.0057 1 Simplif. = 1.0057 m Let 1 = m, the number of months. The epression 1.0057 m represents the equivalent monthl increase of spending. PearsonTEXAS.com 397

Problem 3 Compound Interest Finance Suppose that when our friend was born, our friend s parents deposited $000 in an account paing 4.5% interest compounded quarterl. What will the account balance be after 18 r? Is the formula an eponential growth function? Yes. You can rewrite the formula as A = P 311 + r n n 4 t. So, it is an eponential function with initial amount P and growth factor 11 + r n n. $000 principal 4.5% interest interest compounded quarterl A = P(1 + r n) nt Use the compound interest formula. = 000(1 + 0.045 4 ) 4 # 18 Substitute the values for P, r, n, and t. = 000(1.0115) 7 Simplif. The balance will be $4475.53 after 18 r. Account balance in 18 r Use the compound interest formula. Problem 4 Writing an Eponential Deca Function How do the equations for eponential growth and deca functions compare? The general equation for both functions is f () = ab, but b 7 1 for growth, and 0 6 b 6 1 for deca. The value of a function decreases b a factor of 0.3 with ever unit increase in. When is 0, the value of the function is 1. Write an eponential function in the form f () = ab to describe the situation. f () = ab f () = 1 # b f () = 1 # 0.3 Write the equation for eponential deca. Substitute 1 for a, the initial amount or f(0). Substitute 0.3 for b, the factor b which f() decreases for ever unit increase in. The function that describes the situation is f () = 1 # 0.3. Problem 5 Graphing an Eponential Deca Function Graph the function = 3 ~ 0.5. Identif the -intercept and the asmptote. The equation = 3 # 0.5 is in the form = a # b, where a = 3 and b = 0.5. Since 0 6 b 6 1, the function represents eponential deca. The graph falls from left to right and has a -intercept of 3. The asmptote is the -ais, with the graph approaching the -ais as increases. 5 4 3 1-1 O 1 3 4 5 6 398 Lesson 9- Eponential Growth and Deca

Problem 6 TEKS Process Standard (1)(G) Modeling Eponential Deca STEM Phsics The kilopascal is a unit of measure for atmospheric pressure. The atmospheric pressure at sea level is about 101 kilopascals. For ever 1000-m increase in altitude, the pressure decreases about 11.5%. What is the approimate pressure at an altitude of 3000 m? Will the pressure ever be negative? No. The range of an eponential deca function is all positive real numbers. The graph of an eponential deca function approaches but does not cross the -ais. Relate = a # b Use an eponential function. Define Let = the altitude (in thousands of meters). Let = the atmospheric pressure (in kilopascals). Let a = the initial pressure (in kilopascals), 101. Let b = the deca factor, which is 1-0.115 = 0.885. Write = 101 # 0.885 Use the equation to estimate the pressure at an altitude of 3000 m. = 101 # 0.885 = 101 # 0.885 3 Substitute 3 for. 70 Round to the nearest kilopascal. The pressure at an altitude of 3000 m is about 70 kilopascals. ONLINE H O M E W O R K PRACTICE and APPLICATION EXERCISES Scan page for a Virtual Nerd tutorial video. For additional support when completing our homework, go to PearsonTEXAS.com. 1. Appl Mathematics (1)(A) The value of a stock purchase increases b a factor of 1.5 ever ear. The value of the stock, in dollars, as a function of time, in ears, is given b the equation = 100(1.5). Graph this function and identif the -intercept and the asmptote. What does the -intercept show about the stock?. Appl Mathematics (1)(A) A population of strangler figs, a tpe of vine, was established in the forest man ears ago. The total length of the vines, in feet, over time, in ears, is modeled b the equation = 1() 5. The value = 0 represents the present. Graph this function. What are the -intercept and the asmptote of the graph? What does the -intercept of the graph represent? 3. Eplain Mathematical Ideas (1)(G) An eponential function has the form = a(b) k, where a and b are positive and b 1. Without graphing, how do ou know whether the function will model eponential growth or deca? Eplain our answer. Identif the initial amount a and the growth factor b in each eponential function. 4. g() = 14 # 5. = 150 # 1.0894 6. = 5,600 # 1.01 7. f (t) = 1.4 t PearsonTEXAS.com 399

8. The number of students enrolled at a college is 15,000 and grows 4% each ear. a. The initial amount a is.. b. The percent rate of change is 4%, so the growth factor b is 1 + =. c. To find the number of students enrolled after one ear, ou calculate 15,000 #. d. Complete the equation = # to find the number of students enrolled after ears. e. Use our equation to predict the number of students enrolled after 5 r. 9. Appl Mathematics (1)(A) A population of 100 frogs increases at an annual rate of %. How man frogs will there be in 5 ears? Write an epression to represent the equivalent monthl population increase rate. Find the balance in each account after the given period. 10. $4000 principal earning 6% compounded annuall, after 5 r 11. $1,000 principal earning 4.8% compounded annuall, after 7 r 1. $500 principal earning 4% compounded quarterl, after 6 r 13. $5000 deposit earning 1.5% compounded quarterl, after 3 r 14. $775 deposit earning 4.5% compounded annuall, after 1 r 15. $3500 deposit earning 6.75% compounded monthl, after 6 months Write the eponential function that describes each situation. 16. The value of the function decreases b a factor of 1 with each unit increase in. When = 0, the value of the function is 4. 17. The initial amount of the function is 1, and then it decreases b a factor of 4 5 with each unit increase in. 18. The initial value of the function is 3000, and then it loses 0% of its value with each unit increase in. 19. Eplain Mathematical Ideas (1)(G) The graph of an eponential function passes through the points (3, 100) and (5, 5). Write a function f () = ab that describes this situation. Eplain our reasoning. 0. Appl Mathematics (1)(A) A famil bus a car for $0,000. The value of the car decreases about 0% each ear. After 6 r, the famil decides to sell the car. Should the sell it for $4000? Eplain. 1. Appl Mathematics (1)(A) You invest $100 and epect our mone to grow 8% each ear. About how man ears will it take for our investment to double?. Displa Mathematical Ideas (1)(G) Suppose ou start a lawn-mowing business and make a profit of $400 in the first ear. Each ear, our profit increases 5%. a. Write a function that models our annual profit. b. If ou continue our business for 10 r, what will our total profit be? 400 Lesson 9- Eponential Growth and Deca

Graph the function. Identif the -intercept and the asmptote. 3. f () = 3( 1 ) 4. f () = 0.9( 3) 5. f () = (0.1) + 1 6. Use Multiple Representations to Communicate Mathematical Ideas (1)(D) The graph of an eponential function is decreasing. The -intercept is 300 and the range of the function is 7 60. Sketch a graph of the function, and write a possible equation for the function. Identif the initial amount a and the deca factor b in each eponential function. 7. = 5 # 0.5 8. f () = 10 # 0.1 9. g() = 100( 3) 30. = 0.1 # 0.9 31. Appl Mathematics (1)(A) The population of a cit is 45,000 and decreases % each ear. If the trend continues, what will the population be after 15 r? State whether each graph shows an eponential growth function, an eponential deca function, or neither. 3. 33. STEM 34. Appl Mathematics (1)(A) Radioactive deca is an eample of eponential deca. The half-life of a radioactive substance is the length of time it takes for half of the atoms in a sample of the substance to deca. Cesium-137 is a radioisotope used in radiolog where levels are measured in millicuries (mci). Use the graph at the right. Write the equation for the graph of Cesium-137 deca. What is a reasonable estimate of the half-life of cesium-137? What is the asmptote of the graph? Eplain what it represents. Level (mci) Cesium-137 Deca 500 400 300 00 100 0 0 0 40 60 Time (r) TEXAS End-of-Course PRACTICE 35. A new fitness center opens with 10 members. Ever month the fitness center increases the number of members b 40 members. How man members will the fitness center have after being open for 8 months? 36. What is the slope of the line that passes through the points (1, 1) and (, -1)? 37. What is the simplified form of 5 -? PearsonTEXAS.com 401

9-3 Modeling Eponential Data TEKS FOCUS TEKS (9)(E) Write, using technolog, eponential functions that provide a reasonable fit to data and make predictions for real-world problems. TEKS (1)(E) Create and use representations to organize, record, and communicate mathematical ideas. VOCABULARY Representation a wa to displa or describe information. You can use a representation to present mathematical ideas and data. Additional TEKS (1)(C), (9)(A), (9)(B), (9)(C), (9)(D) ESSENTIAL UNDERSTANDING You can use eponential functions to model some sets of data. When more than three data points suggest an eponential function, ou can use the regression feature of a graphing calculator to find an eponential model. Problem 1 TEKS Process Standard (1)(E) Modeling Real-World Data Transportation The data at the right give the value of a used car over time. Which tpe of function best models the data? Write an equation to model the data. The value of a used car over time The most appropriate model for the data Graph the data and then use differences or ratios to find a model for the situation. Step 1 Step Graph the data. Test for a common ratio. Value of Used Car Years Value ($) 0 1,575 1 11,065 9750 3 850 4 7540 Value ($), 1,000 9000 6000 3000 0 0 4 6 Years, 1 1 1 1 Years Value ($) 0 1,575 1 11,065 9750 3 850 4 7540 11,065 1,575 9750 11,065 850 9750 7540 850 0.88 0.88 0.87 0.88 The graph curves and does not look The value of the car is roughl 0.88 quadratic. It ma be eponential. times its value the previous ear. continued on net page 40 Lesson 9-3 Modeling Eponential Data

Problem 1 continued Step 3 Step 4 Write an eponential model. Test two points other than (0, 1,575). Relate f () = a # b Test (, 9750): Test (4, 7540): Define Let a = the initial value, 1,575. = 1,575 # 0.88 = 1,575 # 0.88 4 Let b = the deca factor, 0.88. 9738 7541 Write f () = 1,575 # 0.88 The point (, 9738) is close to the data point (, 9750). The point (4, 7541) is close to the data point (4, 7540). The equation = 1,575 # 0.88 models the data. Problem TEKS Process Standard (1)(C) Modeling Eponential Data Using Technolog The table shows the numbers of bacteria in a culture after the given numbers of hours. Predict when the number of bacteria will reach 10,000. You can select technolog as a tool to help ou solve this problem. Using a graphing calculator, ou can determine whether an eponential function is a reasonable model. Step 1 Enter the data. L1 L L3 3 1 3 4 5 6 7 05 70 350 653 305 3417 3890 L3(1)= Hour 1 3 4 5 6 7 8 9 10 Bacteria 05 70 350 653 305 3417 3890 45 5107 574 Step Use EpReg. The model is f () = 1779.404(1.11). Step 3 Graph the data and the function to confirm the model. EpReg = a * b^ a = 1779.40359 b = 1.10650954 r =.9800566 r =.98996549 An eponential model is reasonable. continued on net page PearsonTEXAS.com 403

Problem continued How can I see -values that are closer together in the table? Go into the table setup for our calculator. You can change the increment between successive -values. Step 4 Use the model to predict how long it will take for the number of bacteria to reach 10,000. Use tables or the trace feature on the graph. You ma need to adjust the viewing window. X Y1 Since a tenth of an hour is 6 minutes, 15. hours means 15 hours 1 minutes. 15 984.9 15.1 9937.5 15. 10051 15.3 10166 15.4 1083 15.5 10401 15.6 1050 Y1 = 10051.3411708 Y1 = 1779.4035899111 * 1.1 X = 15.157 Y = 1000.9 How does the domain for the real-world data differ from the domain for the function? In the function, could be an real number. The bounce number, however, must come from the set {0, 1,, }. So the domain is the set of whole numbers. The number of bacteria will reach 10,000 at about 15 hours 1 minutes. Problem 3 Analzing Features of Eponential Data A ball is dropped from a height of 75 in. The heights of the ball s rebounds after subsequent bounces are shown in the table. A What is an eponential model for this data? Enter the data into lists in a graphing calculator, and perform an eponential regression on the data. An eponential model for the data is f () = 75 # 0.6. B Identif the domain and range of the function in part (A) in the contet of the problem. Epress the domain and range using inequalities. The domain is the bounce number. The bounce number cannot be negative, so the domain is Ú 0, where is an integer. The range is the height of the rebound. The height starts at 75 in. and then decreases, but cannot be negative. It will get closer and closer to 0, but never reach 0 according to the model. The range is 0 6 f () 75, where f () = 75 # 0.6. C What is the -intercept of the function in part (A), and what does it mean in the contet of the problem? The -intercept is the -value when = 0. When = 0, f () = 75 # 0.6 0 = 75, so the -intercept is 75. In the contet of the problem, this is the height of the ball after drop 0, or the initial height of the ball, 75 in. D An eponential function is a function in the form f () = a ~ b. What are a and b in the function in part (A)? What do a and b mean in the contet of the problem? In the function f () = 75 # 0.6, a = 75, and b = 0.6. Bounce Height of Rebound (in.) Ball Rebounds The value of a is the initial height of the ball, 75 in. The value of b is the ratio between rebounds. Each rebound is 0.6, or 6%, of the height of the previous rebound. 0 75 1 46 9 3 18 4 11 404 Lesson 9-3 Modeling Eponential Data

ONLINE H O M E W O R K PRACTICE and APPLICATION EXERCISES Scan page for a Virtual Nerd tutorial video. For additional support when completing our homework, go to PearsonTEXAS.com. Identif the domain and range of the function. Epress the range using an inequalit. 1. f () = 15 # 1.79 3. f () =-3.5 # 1. f () = 460 # 0.17 4. f () =-4 # 0.999 Find f (0), f (4), and f ( ) for each function. Round to the nearest tenth. 5. f () = 8 #.0 7. f () =-6.4 # 1.49 6. f () = 107 # 0.387 8. f () =-5 # 0.835 9. Select Tools to Solve Problems (1)(C) The table at the right shows the length and weight of a species of fish. a. Select one of the following tools to use to find an eponential model for the data and predict the weight of a fish that is 4 in. long. Eplain our choice. Fish Lengths and Weights Length (in.) Weight (lb) 8 1.0 10 1.40 1 1.64 14 1.9 16.5 paper and pencil technolog manipulatives b. Find an eponential model for the data. Predict the weight of a fish that is 4 in. long. 10. Use Multiple Representations to Communicate Mathematical Ideas (1)(D) A culture is started with 50,000 bacteria, and then an antibiotic is added to the culture. The table at the right shows the number of bacteria after the antibiotic is added. a. Find an eponential model that is a reasonable fit for the data. b. How long will it take for the number of bacteria to fall below 5000? Bacteria Population Time Since Antibiotic Number of Added (hr) Bacteria 0 50,000 1 4,100 35,448 3 9,847 4 5,131 c. What is the -intercept of our function? What does it mean in the contet of the problem? d. What are the values of a and b for our function? What do these values mean in the contet of the problem? e. What are the real-world domain and range of the function? Epress each using inequalities. f. Graph the function. PearsonTEXAS.com 405

11. Select Tools to Solve Problems (1)(C) The table below shows the balance in Mr. Harris s retirement savings account for several ears after he retired. Retirement Account Balance Years Since Retirement Balance ($) 0 75,000 1 65,375 56,087 3 47,14 4 38,475 a. Use technolog to find an eponential model that is a reasonable fit for the data. b. Predict when the balance will be less than $100,000, assuming that the pattern continues. 1. Use Representations to Communicate Mathematical Ideas (1)(E) Samantha took out a loan that does not require her to make an paments for 1 months, although interest is being charged to her account. The table below shows the total amount she owes each month after taking the loan. Loan Balance Month 0 1 3 4 Total Amount Owed ($) 3700 375 3808 3858 391 a. Find an eponential model that is a reasonable fit for the data. b. How much will Samantha owe at the end of 1 months, assuming she does not make an paments before then? c. What is the -intercept of our function? What does it mean in the contet of the problem? d. What are the values of a and b for our function? What do these values mean in the contet of the problem? e. What are the real-world domain and range of the function? Epress each using inequalities. f. Graph the function. 13. Appl Mathematics (1)(A) The function f () = 0.973 # 1.187 represents the value in millions of dollars of a software compan, where is the number of ears since the compan was started. a. What is the -intercept of the function, and what does it mean in the contet of the problem? b. What are the a and b values of the function, and what do these values mean in the contet of the problem? c. According to the model, predict what the value of the compan will be 10 ears after it was started. 406 Lesson 9-3 Modeling Eponential Data

14. The function f () = 346 # 0.95 represents the population of a town, where is the number of ears since 1996. a. What is the -intercept of the function, and what does it mean in the contet of the problem? b. What are the a and b values of the function, and what do these values mean in the contet of the problem? c. According to the model, predict what the population will be in 00. For f () = a ~ b, determine whether each statement is alwas, sometimes, or never true. 15. The -intercept is a. 16. The value of f () increases as the value of increases. 17. If a 7 0 and b 7 0, the graph of the function is entirel in Quadrant 1 of the coordinate plane. 18. The range includes negative numbers. TEXAS End-of-Course PRACTICE 19. What is the range of f () = 43 #.4? A. f () 7 0 B. f () 7.4 C. f () 7 103. D. 0 6 f () 6 43 0. The function f () = 4,950 # 0.793 models the value of a car, where is the age of the car in ears. How old will the car be when the value of the car becomes less than $5000? F. ears G. 3 ears H. 5 ears J. 7 ears 1. The value of Edward s savings account is modeled b the function f () = 975 # 1.08, where is the number of ears since the account was opened. In how man ears will the account value be double the original amount? A. 0 B. 5 C. 30 D. 35. The table shows the number of contestants remaining after each round of a singing competition. What is an eponential model for the data? Use our model to predict how man rounds are required to select a single winner. Round Number of Contestants Remaining Singing Competition 0 150 1 90 54 3 3 4 19 PearsonTEXAS.com 407

Topic 9 Review TOPIC VOCABULARY asmptote, p. 386 p. 396 p. 396 p. 396, p. 386 p. 395 p. 395 Check Your Understanding Choose the correct term to complete each sentence. 1. For a function = a # b, where a 7 0 and b 7 1, b is the?.. For a function = a # b, where a 7 0 and 0 6 b 6 1, b is the?. 3. The function = a # b models? for a 7 0 and b 7 1. 4. The function = a # b models? for a 7 0 and 0 6 b 6 1. 9-1 Eponential Functions Quick Review An eponential function involves repeated multiplication of an initial amount a b the same positive number b. The general form of an eponential function is = a # b, where a 0, b 7 0, and b 1. Eample What is the graph of = 1 ~ 5? Make a table of values. Graph the ordered pairs. 1 0 1 1 50 1 10 1 5 5 6 4 O Eercises Evaluate each function for the domain 51,, 36. 5. f () = 4 6. = 0.01 7. = 40 ( 1 ) 8. f () = 3 # Graph each function. 9. f () =.5 10. = 0.5(0.5) 11. f () = 1 # 3 1. = 0.1 13. A population of 50 bacteria in a laborator culture doubles ever 30 min. The function p() = 50 # models the population, where is the number of 30-min periods. a. How man bacteria will there be after h? b. How man bacteria will there be after 1 da? 408 Topic 9

9- Eponential Growth and Deca Quick Review When a 7 0 and b 7 1, the function = a # b models eponential growth. The base b is called the growth factor. When a 7 0 and 0 6 b 6 1, the function = a # b models eponential deca. In this case the base b is called the deca factor. Eample The population of a cit is 5,000 and decreases 1% each ear. Predict the population after 6 r. = 5,000 # 0.99 Eponential deca function = 5,000 # 0.99 6 Substitute 6 for. 3,537 Simplif. The population will be about 3,537 after 6 r. Eercises Tell whether the function represents eponential growth or eponential deca. Identif the growth or deca factor. 14. = 5. # 3 15. f () = 7 # 0.3 16. = 0.15 ( 3 ) 17. g() = 1.3 ( 1 4 ) 18. Suppose $000 is deposited in an account paing.5% interest compounded quarterl. What will the account balance be after 1 r? 19. A band performs a free concert in a local park. There are 00 people in the crowd at the start of the concert. The number of people in the crowd grows 15% ever half hour. How man people are in the crowd after 3 h? Round to the nearest person. 9-3 Modeling Eponential Data Quick Review For some data, an eponential model is a good fit. You can enter the data into our calculator and use the regression feature to find an eponential model. You can then use our model to answer questions about the data b eamining the graphs or tables, or b using the function. Eponential functions are written in the form f () = a # b. Eample The table shows the value of a computer. Find an eponential model, and find the computer s value after 7 ears. Eercises The table shows the population of geese in a park beginning in the ear 003. Use the table to answer Eercises 0 5. Geese Population Year Population 0 58 1 61 65 0. Find an eponential model to best fit the data. 1. Predict the population in the ear 015.. According to the model, in what ear will the population first be greater than 150 geese? 3 69 4 73 Age Value ($) Computer Value 0 00 1 138 868 3 545 4 34 3. What is the -intercept of our function, and what does it mean in the contet of the problem? 4. What are the a and b values of our function, and what do the mean in the contet of the problem? The data appear to be eponential. The calculator gives a regression model of f () = 00 # 0.68. Use the table and the eponential model to see that the computer will be worth about $85 after 7 ears. 5. What are the real-world domain and range of the function? PearsonTEXAS.com 409

Topic 9 TEKS Cumulative Practice Multiple Choice Read each question. Then write the letter of the correct answer on our paper. 1. If the graph of the function = - 6 were shifted 3 units down, which equation could represent the shifted graph? A. = 3-6 C. = - 9 B. = - 3 D. = 3-3. Which ordered pair is a solution of 3-6 0? F. (7, 1) H. (8, 0) G. (5, -6) J. (-1, -4) 3. Brianna has a clindrical glass that is 15 cm tall. The diameter of the base is 5 cm. About how much water can the glass hold? A. 75 cm 3 C. 95 cm 3 B. 118 cm 3 D. 1178 cm 3 4. What is the solution of this sstem of equations? -3 + =- + =-6 F. (-, -6) H. (1, 5) G. ( -1, -5) J. ( -3, -) 5. Jeremiah made the graph at the right to show how much mone he saved after working for a few months. Which of the following represents the amount of mone Jeremiah had when he started working? A. -intercept B. -intercept C. slope D. domain Savings, Savings $00 $150 $100 $50 $0 0 1 3 4 Month, 6. Eduardo is drawing the graph of a function. Each time the -value increases b 3, the -value decreases b 4. The function includes the point (1, 3). Which could be Eduardo s graph? F. 4 O G. 4 O H. 4 O J. 5 7. The data shown in the table at the right represent points on a line. What is the -intercept of the line? A. -5 B. -3 C. 0 D..5 O 4 4 8. What is the factored form of 3 + - 8? F. ( + ) (3-8) G. ( + 4) (3 - ) H. ( + ) (3-4) J. (3 + ) ( - 4) 9. The formula for the area A of a circle is A = pr, where r is the radius of the circle. Which equation can be used to find the radius? A. r = 1Ap p C. r = A p B. r = A p D. r = 1Ap 3 4 5 1 1 3 5 410 Topic 9 TEKS Cumulative Practice

10. Which function has -values that alwas increase when the corresponding -values increase? F. = 0 0 + G. = + H. = + J. =- - 1 11. What is the solution of this sstem of equations? + = 3 4 - =-7 A. (1, 11) C. (-1, -11) B. (-11, 1) D. (11, 1) Gridded Response 1. The formula h =-16t + c can be used to find the height h, in feet, of a falling object t seconds after it is dropped from a height of c feet. Suppose an object falls from a height of 40 ft. How long, in seconds, will the object take to reach the ground? Round our answer to the nearest tenth. 13. A 5-foot ladder rests against a wall. The top of the ladder reaches 0 feet high on the wall. How far awa from the wall is the bottom of the ladder in feet? 0 ft 5 ft Constructed Response 17. The list below shows the heights, in inches, of the students in Core s class. 60, 64, 58, 57, 60, 65, 51, 53, 57, 56 How man students are more than 5 ft tall? 18. Write the sstem of inequalities for the graph below. Show our work. 4 4 O 4 4 19. Mr. Wong drove to the grocer store. The graph at the right shows his distance from home during the drive. How man times did Mr. Wong stop the car before reaching the grocer store? 0. The volume of a rectangular prism is 70 in. 3. The height of the prism is 10 in. The width is 4 in. What is the length, in inches? 1. What is the slope of the line below? 6 Distance Time 14. What is the fifth term in the sequence below? 3.5, 4, 4.75, 5.5, c 15. What is the solution of the following proportion? -a - 3(a - ) 4 = 6 16. Mariah made a model of a square pramid. The height h of the pramid is 6 in. The area of the base B is 36 in.. What is the volume V, in cubic inches, of the pramid? Use the formulav = 1 3 Bh. 4 O 4. Your cellphone plan costs $39.99 per month plus $.10 for ever tet message that ou receive or send. This month, ou receive 7 tet messages and send 10 tet messages. What is our bill, in dollars, for this month? PearsonTEXAS.com 411

Additional Practice Topic 9 Lesson 9-1 Evaluate each function over the domain { 1, 0, 1, }. As the values of the domain increase, do the values of the function increase or decrease? 1. = 3. = ( 3 4) 3. = 1.5 4. = ( 1 ) # 3 5. =-3 # 7 6. =-(4) 7. = 3 # ( 1 5) 8. = 9. = # 3 10. = (0.8) 11. =.5 1. =-4 # (0.) Graph each eponential function. Identif the domain, range, -intercept, and asmptote. 13. = 1 # 3 14. =-4 # 15. = 4 # (0.3) Write and solve an eponential equation to answer each question. 16. Suppose an investment of $5,000 doubles ever 1 ears. How much is the investment worth after 36 ears? After 48 ears? 17. Suppose 15 animals are taken to an island, and then their population triples ever 8 months. How man animals will there be in 4 ears? 18. The population of a cit this ear is 34,500. The population is epected to grow b 3% each ear. What will the population of the cit be in 1 ears? Lesson 9- Identif each function as eponential growth or eponential deca. Then identif the growth factor or deca factor. 19. = 8 0. = 3 4 1. = 9( 1 ). = 4 # 9 3. = 0.65 4. = 3 # 1.5 5. = 5( 1 4) 6. = 0.1 # 0.9 7. = 0.7 # 3.3 Graph each eponential function, and identif the -intercept and the asmptote. 8. = 1 ( 1 4) 9. = 4 # (0.) 30. = 3.5 48 Additional Practice

Lesson 9- continued Write an eponential function that describes each situation. 31. The value of a function decreases b a factor of 0.6 with ever unit increase in. When = 0, the value of the function is 10. 3. The value of a function increases b a factor of 8.5%. When = 0, the value of the function is. Write an eponential function that describes each situation. Find the balance in each account after the given period. 33. $00 principal earning 4% compounded annuall, after 5 ears 34. $1000 principal earning 3.6% compounded monthl, after 10 ears 35. $3000 investment losing 8% compounded annuall, after 3 ears Additional Practice Find the balance in each account. 36. You deposit $500 in a savings account with 3% interest compounded annuall. What is the balance in the account after 6 ears? 37. You deposit $750 in an account with 7% interest compounded semiannuall. What is the balance in the account after 4 ears? 38. You deposit $50 in an account with 4% interest compounded monthl. What is the balance in the account after 5 ears? Lesson 9-3 39. The table shows the population (in thousands) of the countr of Algeria from 1950 to 1990, where is the number of ears since 1950. Year Since 1950 0 5 10 15 0 5 30 35 40 Population (thousands) 8893 984 10,909 11,963 1,93 16,140 18,806,008 5,190 SOURCE: United States Census Bureau a. Find an eponential model that is a reasonable fit for the data. b. What is the predicted population of Algeria in 00, assuming that this trend continues? 40. Camilla had a collection of 140 coins from all over the world. She decided to give some coins awa to friends. The table below shows the number of coins remaining in her collection. Da 0 1 3 4 Number of Coins 140 10 76 55 33 a. Find an eponential model that is a reasonable fit for the data. b. How man coins will Camilla have left after 7 das, assuming that her pattern continues? PearsonTEXAS.com 49

Reference Table 1 Measures Length United States Customar 1 inches (in.) = 1 foot (ft) 36 in. = 1 ard (d) 3 ft = 1 ard 580 ft = 1 mile (mi) 1760 d = 1 mile Metric 10 millimeters (mm) = 1 centimeter (cm) 100 cm = 1 meter (m) 1000 mm = 1 meter 1000 m = 1 kilometer (km) Area 144 square inches (in. ) 9 ft 43,560 ft 4840 d = 1 square foot (ft ) = 1 square ard (d ) = 1 acre (a) = 1 acre 100 square millimeters (mm ) = 1 square centimeter (cm ) 10,000 cm = 1 square meter (m ) 10,000 m = 1 hectare (ha) Reference Volume 178 cubic inches (in. 3 ) 7 ft 3 = 1 cubic foot (ft 3 ) = 1 cubic ard (d 3 ) Liquid Capacit 8 fluid ounces (fl oz) = 1 cup (c) c = 1 pint (pt) pt = 1 quart (qt) 4 qt = 1 gallon (gal) 1000 cubic millimeters (mm 3 ) = 1 cubic centimeter (cm 3 ) 1,000,000 cm 3 = 1 cubic meter (m 3 ) 1000 milliliters (ml) = 1 liter (L) 1000 L = 1 kiloliter (kl) Weight or Mass 16 ounces (oz) = 1 pound (lb) 000 pounds = 1 ton (t) 1000 milligrams (mg) = 1 gram (g) 1000 g = 1 kilogram (kg) 1000 kg = 1 metric ton Temperature 3 F = freezing point of water 98.6 F = normal human bod temperature 1 F = boiling point of water 0 C = freezing point of water 37 C = normal human bod temperature 100 C = boiling point of water Customar Units and Metric Units Length Capacit Weight and Mass 1 in. =.54 cm 1 mi 1.61 km 1 ft 0.305 m 1 qt 0.946 L 1 oz 8.4 g 1 lb 0.454 kg 60 seconds (s) = 1 minute (min) 60 minutes = 1 hour (h) 4 hours = 1 da (d) 7 das = 1 week (wk) Time 4 weeks (appro.) = 1 month (mo) 365 das = 1 ear (r) 5 weeks (appro.) = 1 ear 1 months = 1 ear 10 ears = 1 decade 100 ears = 1 centur 430 Reference

Table Reading Math Smbols Smbols Words # multiplication sign, times ( ) Smbols Words 1 a, a 0 reciprocal of a = equals Are the statements equal? is approimatel equal to is not equal to < is less than > is greater than is less than or equal to is greater than or equal to is congruent to { plus or minus ( ) parentheses for grouping [ ] brackets for grouping { } set braces % percent a c absolute value of a and so on - a opposite of a p pi, an irrational number, approimatel equal to 3.14 degree(s) a n nth power of a nonnegative square root of a n 1 a n, a 0 < > AB line through points A and B AB AB A m A ABC (, ) segment with endpoints A and B length of AB; distance between points A and B angle A measure of angle A triangle ABC ordered pair 1,,... specific values of the variable 1,,... specific values of the variable f() f of ; the function value at m slope of a line b -intercept of a line a : b ratio of a to b ^ raised to a power (in a spreadsheet formula) * multipl (in a spreadsheet formula) / divide (in a spreadsheet formula) Reference PearsonTEXAS.com 431

Properties and Formulas Reference Order of Operations 1. Perform an operation(s) inside grouping smbols.. Simplif powers. 3. Multipl and divide from left to right. 4. Add and subtract from left to right. Commutative Propert of Addition For ever real number a and b, a + b = b + a. Commutative Propert of Multiplication For ever real number a and b, a # b = b # a. Associative Propert of Addition For ever real number a, b, and c, (a + b) + c = a + (b + c). Associative Propert of Multiplication For ever real number a, b, and c, (a # b) # c = a # (b # c). Identit Propert of Addition For ever real number a, a + 0 = a. Identit Propert of Multiplication For ever real number a, 1 # a = a. Multiplication Propert of 1 For ever real number a, - 1 # a = - a. Zero Propert of Multiplication For ever real number a, a # 0 = 0. Inverse Propert of Addition For ever real number a, there is an additive inverse - a such that a + ( - a) = 0. Inverse Propert of Multiplication For ever nonzero number a, there is a multiplicative inverse such that a # 1 a = 1. Distributive Propert For ever real number a, b, and c: a(b + c) = ab + ac (b + c)a = ba + ca a(b - c) = ab - ac (b - c)a = ba - ca Addition Propert of Equalit For ever real number a, b, and c, if a = b, then a + c = b + c. Subtraction Propert of Equalit For ever real number a, b, and c, if a = b, then a - c = b - c. Multiplication Propert of Equalit For ever real number a, b, and c, if a = b, then a # c = b # c. Division Propert of Equalit For ever real number a, b, and c, where c 0, if a = b, then a c = b c. Percent Proportion, where b 0. a b = p 100 Percent Equation a = p% # b, where b 0. Simple Interest Formula I = prt Percent of Change amount of increase or decrease p% = original amount amount of increase = new amount - original amount amount of decrease = original amount - new amount Relative Error relative error = 0 measured or estimated value - actual value 0 actual value The following properties of inequalit are also true for Ú and. Addition Propert of Inequalit For ever real number a, b, and c, if a 7 b, then a + c 7 b + c; if a 6 b, then a + c 6 b + c. Subtraction Propert of Inequalit For ever real number a, b, and c, if a 7 b, then a - c 7 b - c; if a 6 b, then a - c 6 b - c. Multiplication Propert of Inequalit For ever real number a, b, and c, where c 7 0, if a 7 b, then ac 7 bc; if a 6 b, then ac 6 bc. For ever real number a, b, and c, where c 6 0, if a 7 b, then ac 6 bc; if a 6 b, then ac 7 bc. Division Propert of Inequalit For ever real number a, b, and c, where c 7 0, if a 7 b, then a c 7 b c ; if a 6 b, then a c 6 b c. For ever real number a, b, and c, where c 6 0, if a 7 b, then a c 6 b c ; if a 6 b, then a c 7 b c. 43 Reference

Refleive Propert of Equalit For ever real number a, a = a. Smmetric Propert of Equalit For ever real number a and b, if a = b, then b = a. Transitive Propert of Equalit For ever real number a, b, and c, if a = b and b = c, then a = c. Transitive Propert of Inequalit For ever real number a, b, and c, if a 6 b and b 6 c, then a 6 c. Topic 1 Solving Equations and Inequalities Distance Traveled d = rt Temperature C = 5 (F - 3) 9 Cross Products of a Proportion If a b = c, where b 0 and d 0, then ad = bc. d Standard Form of a Linear Equation The standard form of a linear equation is A + B = C, where A, B, and C are real numbers and A and B are not both zero. Slopes of Parallel Lines Nonvertical lines are parallel if the have the same slope and different -intercepts. An two vertical lines are parallel. Slopes of Perpendicular Lines Two lines are perpendicular if the product of their slopes is - 1. A vertical line and horizontal line are perpendicular. Function Famil: Linear Parent = f() 0 0 0 0 Translate horizontal b c = f ( - c) vertical b d = f () + d Reflection across the -ais across the -ais Slope Change a 7 1, graph steeper 0 6 a 6 1, graph less steep b 7 1, graph steeper 0 6 b 6 1, graph less steep =-f() = f(-) = af () = f (b) Reference Topic An Introduction to Functions Function Notation Functions are represented as equations involving and, such as = + 3. The same equation can be written in function notation f() = + 3. Notice f () replaces and is read f of. The letter f is the name of the function, not a variable. Topic 3 Linear Functions Slope slope = vertical change horizontal change = rise run Direct Variation A direct variation is a relationship that can be represented b a function of the form = k, where k 0. Slope-Intercept Form of a Linear Equation The slope-intercept form of a linear equation is = m + b, where m is the slope and b is the -intercept. Point-Slope Form of a Linear Equation The point-slope form of the equation of a nonvertical line that passes through the point ( 1, 1 ) with slope m is - 1 = m( - 1 ). Topic 4 Sstems of Equations and Inequalities Solutions of Sstems of Linear Equations A sstem of linear equations can have one solution, no solution, or infinitel man solutions: If the lines have different slopes, the lines intersect, so there is one solution. If the lines have the same slopes and different -intercepts, the lines are parallel, so there are no solutions. Topic 5 Eponents and Radicals Zero as an Eponent For ever nonzero number a, a 0 = 1. PearsonTEXAS.com 433

Reference Negative Eponent For ever nonzero number a and rational number n, a - n = 1 a n. Multipling Powers With the Same Base For ever nonzero number a and rational numbers m and n, a m # a n = a m+n. Dividing Powers With the Same Base For ever nonzero number a and rational numbers m and n, a m a n = a m-n. Raising a Power to a Power For ever nonzero number a and rational numbers m and n, (a m ) n = a mn. Raising a Product to a Power For ever nonzero number a and b and rational number n, (ab) n = a n b n. Raising a Quotient to a Power For ever nonzero number a and b and rational number n, ( a b) n = an b n. Properties of Rational Eponents If the nth root of a is a real number and m is an integer, then 1 a n = 1 n a and m a n = n a 0. a m = ( 1 n a ) m. If m is negative, Multiplication Propert of Square Roots For ever number a Ú 0 and b Ú 0, ab = a # b. Division Propert of Square Roots For ever number a Ú 0 and b 7 0, 5 a b = 1a 1b. The Pthagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hpotenuse: a + b = c. The Converse of the Pthagorean Theorem If a triangle has sides of lengths a, b, and c, and a + b = c, then the triangle is a right triangle with hpotenuse of length c. Topic 6 Sequences Arithmetic Sequence The eplicit formula for an arithmetic sequence is A(n) = A(1) + (n - 1)d, where A(n) is the nth term, A(1) is the first term, n is the term number, and d is the common difference. The recursive definition for an arithmetic sequence with common difference d has two parts: A(1) = first term Initial condition, or starting value A(n) = A(n - 1) + d, for n Ú Recursive formula Geometric Sequence The eplicit formula for a geometric sequence is A(n) = A(1) # r n - 1, where A(n) is the nth term, A(1) is the first term, n is the term number, and r is the common ratio. The recursive definition for a geometric sequence with common ratio r has two parts: A(1) = a A(n) = A(n 1) # r, for n Ú Initial condition, or starting value Recursive formula Topic 7 Polnomials and Factoring Factoring Special Cases For ever nonzero number a and b: a - b = (a + b)(a - b) a + ab + b = a + b)(a + b = a + b) a - ab + b = a - b)(a - b = a - b) Topic 8 Quadratic Functions and Equations Graph of a Quadratic Function The graph of = a + b + c, where a 0, has the line = -b a as its ais of smmetr. The -coordinate of the verte is -b a. Function Famil: Quadratic Parent = Translation horizontal = ( - c) c 7 0, c units right c 6 0, 0 c 0 units left vertical d 7 0, d units up d 6 0, 0 d 0 units down = + d Stretch, Compression, and Reflection horizontal = (b) compression ( 0 b 0 7 1) stretch (0 6 0 b 0 6 1) reflection across the -ais (b 6 0) vertical = a() stretch ( 0 a 0 7 1) compression (0 6 0 a 0 6 1) reflection across the -ais (a 6 0) 434 Reference

Verte Form of a Quadratic Function The quadratic function f() = a( - h) + k is written in verte form. Ais of smmetr: = h Verte: (h, k) Maimum or minimum value: k Zero-Product Propert For ever real number a and b, if ab = 0, then a = 0 or b = 0. Completing the Square B adding ( b ) to the epression + b, it forms a perfect-square trinomial. + b + ( b ) = ( + b ) Quadratic Formula If a + b + c = 0, where a 0, then = -b { b - 4ac a. Propert of the Discriminant For the quadratic equation a + b + c = 0, where a 0, the value of the discriminant b - 4ac tells ou the number of solutions. If b - 4ac 7 0, there are two real solutions. If b - 4ac = 0, there is one real solution. b - 4ac 6 Topic 9 Eponential Functions and Equations Eponential Function An eponential function is a function of the form = a # b, where a 0, b 7 0, b 1, and is a real number. The horizontal asmptote for an eponential function of the form = a # b is the -ais ( = 0). Compound Interest Formula A = P(1 + r n) nt Eponential Growth and Deca An eponential function has the form = a # b, where a is a nonzero constant, b is greater than 0 and not equal to 1, and is a real number. The function = a # b, where b is the growth factor, models eponential growth for a 7 0 and b 7 1. The function = a # b, where b is the deca factor, models eponential deca for a 7 0 and 0 6 b 6 1. Reference PearsonTEXAS.com 435

Formulas of Geometr You will use a number of geometric formulas as ou work through our algebra book. Here are some perimeter, area, and volume formulas. / P = / + w A = /w w P = 4s A = s s Rectangle Square Reference d r h h C = pr or C = pd A = pr b A = 1 bh b A = bh Circle Triangle Parallelogram b 1 h b A = 1 (b 1 + b )h Trapezoid / V = Bh V = /wh Right Prism w h h V = 1 3 Bh Pramid base r h base h r r base V = Bh V = pr h Right Clinder V = 1 3 Bh V = 1 3 pr h Right Cone V = 4 3 pr 3 Sphere 436 Reference

Visual Glossar English A Spanish Arithmetic sequence (p. 46) A number sequence formed b adding a fied number to each previous term to find the net term. The fied number is called the common difference. Eample 4, 7, 10, 13, c is an arithmetic sequence. Progresión aritmética (p. 46) En una progresión aritmética la diferencia entre términos consecutivos es un número constante. El número constante se llama la diferencia común. Asmptote (p. 384) A line that the graph of a function gets closer to as or gets larger in absolute value. Asíntota (p. 384) Línea recta a la que la gráfica de una función se acerca indefinidamente, mientras el valor absoluto de o aumenta. Eample 1 O Ais of smmetr (p. 36) The line that divides a parabola into two matching halves. Eample The -ais is a vertical asmptote for = 1. The -ais is a horizontal asmptote for = 1. O ais of smmetr Eje de simetría (p. 36) El eje de simetría es la línea que divide una parábola en dos mitades eactamente iguales. Visual Glossar B Binomial (p. 68) A polnomial of two terms. Binomio (p. 68) Polinomio compuesto de dos términos. Eample 3 + 7 is a binomial. C Causation (p. 144) When a change in one quantit causes a change in a second quantit. A correlation between quantities does not alwas impl causation. Causalidad (p. 144) Cuando un cambio en una cantidad causa un cambio en una segunda cantidad. Una correlación entre las cantidades no implica siempre la causalidad. Common difference (p. 46) The difference between consecutive terms of an arithmetic sequence. Eample The common difference is 3 in the arithmetic sequence 4, 7, 10, 13, c Diferencia común (p. 46) La diferencia común es la diferencia entre los términos consecutivos de una progresión aritmética. PearsonTEXAS.com 437

English Common ratio (p. 46) The fied number used to find terms in a geometric sequence. Spanish Razón común (p. 46) Número constante que se usa para hallar los términos en una progresión geométrica. Eample The common ratio is 1 3 in the geometric sequence 9, 3, 1, 1 3, c Completing the square (p. 367) A method of solving quadratic equations. Completing the square turns ever quadratic equation into the form = c. Completar el cuadrado (p. 367) Método para solucionar ecuaciones cuadráticas. Cuando se completa el cuadrado, se transforma la ecuación cuadrática a la fórmula = c. Eample + 6-7 = 9 is rewritten as ( + 3) = 5 b completing the square. Compound inequalities (p. 40) Two inequalities that are joined b and or or. Eamples 5 6 and 6 10 14 6 or -3 Desigualdades compuestas (p. 40) Dos desigualdades que están enlazadas por medio de una o una o. Visual Glossar Compound interest (p. 395) Interest paid on both the principal and the interest that has alread been paid. Compression (p. 340) A compression is a transformation that decreases the distance between corresponding points of a graph. Eample For an initial deposit of $1000 at a 6% interest rate with interest compounded quarterl, the function = 10001 0.06 4 gives the account balance after ears. Interés compuesto (p. 395) Interés calculado tanto sobre el capital como sobre los intereses a pagados. Compresión (p. 340) Una compresión es una transformación que disminue la distancia entre puntos que se corresponden en una gráfica. Consistent sstem (p. 160) A sstem of equations that has at least one solution is consistent. Eample Sistema consistente (p. 160) Un sistema de ecuaciones que tiene por lo menos una solución es consistente. O Constant of variation for direct variation (p. 108) The nonzero constant k in the function = k. Eample For the direct variation = 4, 4 is the constant of variation. Constante de variación en variaciones directas (p. 108) La constante k cuo valor no es cero en la función = k. 438 Visual Glossar

English Continuous graph (p. 70) A graph that is unbroken. Eample Spanish Gráfica continua (p. 70) Una gráfica continua es una gráfica ininterrumpida. O Correlation coefficient (p. 144) A number from -1 to 1 that tells ou how closel the equation of the line of best fit models the data. Coeficiente de correlación (p. 144) Número de -1 a 1 que indica con cuánta eactitud la línea de mejor encaje representa los datos. Eample LinReg a b Cross products (of a proportion) (p. ) In a proportion a b = c d, the products ad and bc. These products are equal. r r = a+b =.013403913 =.3603167 =.88637776 =.941449867 The correlation coefficient is approimatel 0.94. Eample The cross products for 3 4 = 6 8 are 3 # 8 and 4 # 6. Productos cruzados (de una proporción) (p. ) En una proporción a b = c, los productos ad bc. Estos productos son d iguales. Visual Glossar D Deca factor (p. 395) 1 minus the percent rate of change, epressed as a decimal, for an eponential deca situation. Eample The deca factor of the function = 5(0.3) is 0.3. Factor de decremento (p. 395) 1 menos la tasa porcentual de cambio, epresada como decimal, en una situación de reducción eponencial. Degree of a monomial (p. 68) The sum of the eponents of the variables of a monomial. Grado de un monomio (p. 68) La suma de los eponentes de las variables de un monomio. Eample -4 3 is a monomial of degree 5. PearsonTEXAS.com 439

English Degree of a polnomial (p. 68) The highest degree of an term of the polnomial. Spanish Grado de un polinomio (p. 68) El grado de un polinomio es el grado maor de cualquier término del polinomio. Dependent sstem (p. 160) A sstem of equations that does not have a unique solution. Dependent variable (p. 59) A variable that provides the output values of a function. Eample The polnomial P () = 6 + 3-3 has degree 6. Eample The ssteme = + 3 represents two -4 + = 6 equations for the same line, so it has man solutions. It is a dependent sstem. Eample In the equation = 3, is the dependent variable. Sistema dependiente (p. 160) Sistema de ecuaciones que no tiene una solución única. Variable dependiente (p. 59) Variable de la que dependen los valores de salida de una función. Visual Glossar Difference of two squares (p. 96) A difference of two squares is an epression of the form a - b. It can be factored as (a + b)(a - b). Direct variation (p. 108) A linear function defined b an equation of the form = k, where k 0. Eamples 5a - 4 = (5a + )(5a - ) m 6-1 = (m 3 + 1)(m 3-1) Eample = 18 is a direct variation. Diferencia de dos cuadrados (p. 96) La diferencia de dos cuadrados es una epresión de la forma a - b. Se puede factorizar como (a + b)(a - b). Variación directa (p. 108) Una función lineal definida por una ecuación de la forma = k, donde k 0, representa una variación directa. Discrete graph (p. 70) A graph composed of isolated points. Eample Gráfica discreta (p. 70) Una gráfica discreta es compuesta de puntos aislados. O Discriminant (p. 37) The discriminant of a quadratic equation of the form a + b + c = 0 is b - 4ac. The value of the discriminant determines the number of solutions of the equation. Discriminante (p. 37) El discriminante de una ecuación cuadrática a + b + c = 0 es b - 4ac. El valor del discriminante determina el número de soluciones de la ecuación. Eample The discriminant of + 9 - = 0 is 97. 440 Visual Glossar

English Spanish Domain (of a relation or function) (p. 83) The possible values for the input of a relation or function. E Elimination method (p. 175) A method for solving a sstem of linear equations. You add or subtract the equations to eliminate a variable. Eample In the function f () = +, the domain is all real numbers. Dominio (de una relación o función) (p. 83) Posibles valores de entrada de una relación o función. Eliminación (p. 175) Método para resolver un sistema de ecuaciones lineales. Se suman o se restan las ecuaciones para eliminar una variable. Eample 3 + = 19 - = 1 5 + 0 = 0 Add the equations to get = 4. (4) - = 1 S Substitute 4 for in 8 - = 1 the second equation. = 7 S Solve for. Ecluded value (p. 305) A value of for which a rational epression f () is undefined. Eplicit formula (p. 46) An eplicit formula epresses the nth term of a sequence in terms of n. Eponential deca (p. 395) A situation modeled with a function of the form = ab, where a 7 0 and 0 6 b 6 1. Eample Let a n = n + 5 for positive integers n. If n = 7, then a 7 = (7) + 5 = 19. Eample = 5(0.1) Valor ecluido (p. 305) Valor de para el cual una epresión racional es indefinida. Fórmula eplícita (p. 46) Una fórmula eplícita epresa el n-ésimo término de una progresión en función de n. Decremento eponencial (p. 395) Para a 7 0 0 6 b 6 1, la función = ab representa el decremento eponencial. Visual Glossar Eponential function (p. 386) A function that repeatedl multiplies an initial amount b the same positive number. You can model all eponential functions using = ab, where a is a nonzero constant, b 7 0, and b 1. Eample eponential deca 0.5 4 Función eponencial (p. 386) Función que multiplica repetidas veces una cantidad inicial por el mismo número positivo. Todas las funciones eponenciales se pueden representar mediante = ab, donde a es una constante con valor distinto de cero, b 7 0 b 1. eponential growth 4 O 4 Eponential growth (p. 395) A situation modeled with a function of the form = ab, where a 7 0 and b 7 1. Eample = 100() Incremento eponencial (p. 395) Para a 7 0 b 7 1, la función = ab representa el incremento eponencial. PearsonTEXAS.com 441

English Etrapolation (p. 144) The process of predicting a value outside the range of known values. Spanish Etrapolación (p. 144) Proceso que se usa para predecir un valor por fuera del ámbito de los valores dados. F Factor b grouping (p. 301) A method of factoring that uses the Distributive Propert to remove a common binomial factor of two pairs of terms. Eample The epression 7( - 1) + 4( - 1) can be factored as (7 + 4)( - 1). Factor común por agrupación de términos (p. 301) Método de factorización que aplica la propiedad distributiva para sacar un factor común de dos pares de términos en un binomio. Falling object model (p. 36) The function h =-16t + c models the height of a falling object, where h is the object s height in feet, t is the time in seconds since the object began to fall, and c is the object s initial height. Modelo de objetos que caen (p. 36) La función h =-16t + c representa la altura de un objeto que cae, donde h es la altura del objeto en pies, t es el tiempo de caída en segundos c es la altura inicial del objeto. Visual Glossar Formula (p. 17) An equation that states a relationship among quantities. Eample The formula for the volume V of a clinder is V = pr h, where r is the radius of the clinder and h is its height. Function (p. 59) A relation that assigns eactl one value in the range to each value of the domain. Eample Earned income is a function of the number of hours worked. If ou earn $4.50/h, then our income is epressed b the function f (h) = 4.5h. Fórmula (p. 17) Ecuación que establece una relación entre cantidades. Función (p. 59) La relación que asigna eactamente un valor del rango a cada valor del dominio. Function notation (p. 88) To write a rule in function notation, ou use the smbol f () in place of. Eample f () = 3-8 is in function notation. Notación de una función (p. 88) Para epresar una regla en notación de función se usa el símbolo f () en lugar de. G Geometric sequence (p. 46) A number sequence formed b multipling a term in a sequence b a fied number to find the net term. Progresión geométrica (p. 46) Tipo de sucesión numérica formada al multiplicar un término de la secuencia por un número constante, para hallar el siguiente término. Eample 9, 3, 1, 1 3,... is an eample of a geometric sequence. 44 Visual Glossar

English Spanish Growth factor (p. 395) 1 plus the percent rate of change for an eponential growth situation. H Eample The growth factor of = 7(1.3) is 1.3. Factor incremental (p. 395) 1 más la tasa porcentual de cambio en una situación de incremento eponencial. Hpotenuse (p. 33) The side opposite the right angle in a right triangle. It is the longest side in the triangle. Hipotenusa (p. 33) En un triángulo rectángulo, el lado opuesto al ángulo recto. Es el lado más largo del triángulo. Eample b A c c is the hpotenuse. C a B I Identit (p. 11) An equation that is true for ever value. Inconsistent sstem (p. 160) A sstem of equations that has no solution. Eample 5-14 = 5(1-14 5 ) is an identit because it is true for an value of. Eample e = + 3 is a sstem of parallel lines, - + = 1 so it has no solution. It is an inconsistent sstem. Identidad (p. 11) Una ecuación que es verdadera para todos los valores. Sistema incompatible (p. 160) Un sistema incompatible es un sistema de ecuaciones para el cual no ha solución. Visual Glossar Independent sstem (p. 160) A sstem of linear equations that has a unique solution. Independent variable (p. 59) A variable that provides the input values of a function. + =-7 Eample e has the unique solution - 3 = 0 ( - 3, - ). It is an independent sstem. Eample In the equation = 3, is the independent variable. Sistema independiente (p. 160) Un sistema de ecuaciones lineales que tenga una sola solución es un sistema independiente. Variable independiente (p. 59) Variable de la que dependen los valores de entrada de una función. PearsonTEXAS.com 443

English Spanish Inde (p. 5) With a radical sign, the inde indicates the degree of the root. Input (p. 59) A value of the independent variable. Eample inde inde 3 inde 4 116 3 16 4 16 Eample The input is an value of ou substitute into a function. Índice (p. 5) Con un signo de radical, el índice indica el grado de la raíz. Entrada (p. 59) Valor de una variable independiente. Interpolation (p. 144) The process of estimating a value between two known quantities. Interpolación (p. 144) Proceso que se usa para estimar el valor entre dos cantidades dadas. L Leg (p. 33) Each of the sides that form the right angle of a right triangle. Cateto (p. 33) Cada uno de los dos lados que forman el ángulo recto en un triángulo rectángulo. Visual Glossar Eample Linear equation (p. 115) An equation whose graph forms a straight line. Eample A b C 4 a c 1 a and b are legs. B Ecuación lineal (p. 115) Ecuación cua gráfica es una línea recta. 1 O 4 Linear factor (p. 360) A linear factor of an epression is a factor in the form a + b, a 0. Linear function (p. 59) A function whose graph is a line is a linear function. You can represent a linear function with a linear equation. Eample Factor lineal (p. 360) Un factor lineal de una epresión es un factor que tiene la forma a + b, a 0. Función lineal (p. 59) Una función cua gráfica es una recta es una función lineal. La función lineal se representa con una ecuación lineal. 1 444 Visual Glossar

English Linear inequalit (p. 187) An inequalit in two variables whose graph is a region of the coordinate plane that is bounded b a line. Each point in the region is a solution of the inequalit. Spanish Desigualdad lineal (p. 187) Una desigualdad lineal es una desigualdad de dos variables cua gráfica es una región del plano de coordenadas delimitado por una recta. Cada punto de la región es una solución de la desigualdad. Eample 1 O Linear parent function (p. 115) The simplest form of a linear function. Eample = Función lineal elemental (p. 115) La forma más simple de una función lineal. Line of best fit (p. 144) The most accurate trend line on a scatter plot showing the relationship between two sets of data. Eample Calories 600 400 Recta de maor aproimación (p. 144) La línea de tendencia en un diagrama de puntos que más se acerca a los puntos que representan la relación entre dos conjuntos de datos. Calories and Fat for Fast Food Meals 00 0 0 10 0 30 40 50 Fat (g) Visual Glossar Literal equation (p. 17) An equation involving two or more variables. Eample 4 + = 18 is a literal equation. Ecuación literal (p. 17) Ecuación que inclue dos o más variables. PearsonTEXAS.com 445

English M Spanish Maimum (p. 36) The -coordinate of the verte of a parabola that opens downward. Eample O Máimo (p. 36) La coordenada del vértice en una parábola que se abre hacia abajo. Since the parabola opens downward, the -coordinate of the verte is the function s maimum value. Visual Glossar Minimum (p. 36) The -coordinate of the verte of a parabola that opens upward. Eample Monomial (p. 68) A real number, a variable, or a product of a real number and one or more variables with whole-number eponents. Mínimo (p. 36) La coordenada del vértice en una parábola que se abre hacia arriba. O Since the parabola opens upward, the -coordinate of the verte is the function s minimum value. Eample 9, n, and -5 are eamples of monomials. Monomio (p. 68) Número real, variable o el producto de un número real una o más variables con números enteros como eponentes. N Negative correlation (p. 144) The relationship between two sets of data, in which one set of data decreases as the other set of data increases. Eample Correlación negativa (p. 144) Relación entre dos conjuntos de datos en la que uno de los conjuntos disminue a medida que el otro aumenta. 0 446 Visual Glossar

English No correlation (p. 144) There does not appear to be a relationship between two sets of data. Eample Spanish Sin correlación (p. 144) No ha relación entre dos conjuntos de datos. Nonlinear function (p. 64) A function whose graph is not a line or part of a line. Eample 0 Función no lineal (p. 64) Función cua gráfica no es una línea o parte de una línea. nth root (p. 5) For an real numbers a and b, and an positive integer n, if a n = b, then a is an nth root of b. Eample O 5 3 = because 5 = 3. 4 81 = 3 because 3 4 = 81. raíz n-ésima (p. 5) Para todos los números reales a b, todo número entero positivo n, si a n = b, entonces a es la n-ésima raíz de b. Visual Glossar O Opposite reciprocals (p. 13) A number of the form - b a, where a is a nonzero rational number. The product of a number b and its opposite reciprocal is -1. Recíproco inverso (p. 13) Número en la forma - b a, donde a es un número racional diferente de cero. El producto de un b número su recíproco inverso es -1. Eample 5 and - 5 are opposite reciprocals because 1 5 1-5 =-1. Output (p. 59) A value of the dependent variable. Salida (p. 59) Valor de una variable dependiente. Eample The output of the function f () = when = 3 is 9. PearsonTEXAS.com 447

English P Spanish Parabola (p. 36) The graph of a quadratic function. Parábola (p. 36) La gráfica de una función cuadrática. Eample O Parallel lines (p. 13) Two lines in the same plane that never intersect. Parallel lines have the same slope. Rectas paralelas (p. 13) Dos rectas situadas en el mismo plano que nunca se cortan. Las rectas paralelas tienen la misma pendiente. Eample O l m Visual Glossar Parent function (p. 115) A famil of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics. Perfect square trinomial (p. 96) An trinomial of the form a + ab + b or a - ab + b. Eample = is the parent function for the famil of linear equations of the form = m + b. Eample ( + 3) = + 6 + 9 Función elemental (p. 115) Una familia de funciones es un grupo de funciones con características en común. La función elemental es la función más simple que reúne esas características. Trinomio cuadrado perfecto (p. 96) Todo trinomio de la forma a + ab + b ó a - ab + b. Perpendicular lines (p. 13) Lines that intersect to form right angles. Two lines are perpendicular if the product of their slopes is -1. Eample l m Rectas perpendiculares (p. 13) Rectas que forman ángulos rectos en su intersección. Dos rectas son perpendiculares si el producto de sus pendientes es -1. Point-slope form (p. 10) A linear equation of a nonvertical line written as - 1 = m( - 1 ). The line passes through the point ( 1, 1 ) with slope m. Forma punto-pendiente (p. 10) La ecuación lineal de una recta no vertical que pasa por el punto ( 1, 1 ) con pendiente m está dada por - 1 = m( - 1 ). Eample An equation with a slope of - 1 passing through (, -1) would be written + 1 =- 1 ( - ) in point-slope form. 448 Visual Glossar

English Polnomial (p. 68) A monomial or the sum or difference of two or more monomials. A quotient with a variable in the denominator is not a polnomial. Spanish Polinomio (p. 68) Un monomio o la suma o diferencia de dos o más monomios. Un cociente con una variable en el denominador no es un polinomio. Eample, 3 + 7, 8, and -7 3 - + 9 are all polnomials. Positive correlation (p. 144) The relationship between two sets of data in which both sets of data increase together. Eample Correlación positiva (p. 144) La relación entre dos conjuntos de datos en la que ambos conjuntos incrementan a la vez. 0 Principal square root (p. 5) A number of the form 1b. The epression 1b is called the principal (or positive) square root of b. Eample 5 is the principal square root of 15. Proportion (p. ) An equation that states that two ratios are equal. Eample 7.5 9 = 5 6 Pthagorean Theorem (p. 33) In an right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hpotenuse: a + b = c. Eample 3 5 3 4 5 Raíz cuadrada principal (p. 5) La epresión 1b se llama raíz cuadrada principal (o positiva) de b. Proporción (p. ) Es una ecuación que establece que dos razones son iguales. Teorema de Pitágoras (p. 33) En un triángulo rectángulo, la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa: a + b = c. Visual Glossar 4 Q Quadratic equation (p. 350) A quadratic equation is one that can be written in the standard form a + b + c = 0, where a 0. Ecuación cuadrática (p. 350) Ecuación que puede epresarse de la forma normal como a + b + c = 0, en la que a 0. Eample 4 + 9-5 = 0 PearsonTEXAS.com 449

English Spanish Quadratic formula (p. 37) If a + b + c = 0 and a 0, then = -b { b - 4ac. a Eample + 10 + 1 = 0 = -b { b - 4ac a = -10 { 10-4()(1) () = -10 { 4 4 = -10 + 4 =- or -3 or -10-4 Fórmula cuadrática (p. 37) Si a + b + c = 0 a 0, entonces = -b { b - 4ac. a Quadratic function (p. 36) A function of the form = a + b + c, where a 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down. Función cuadrática (p. 36) La función = a + b + c, en la que a 0. La gráfica de una función cuadrática es una parábola, o curva en forma de U que se abre hacia arriba o hacia abajo. Eample = 5 - + 1 is a quadratic function. Visual Glossar Quadratic parent function (p. 36) The simplest quadratic function f () = or =. R Eample = is the parent function for the famil of quadratic equations of the form = a + b + c. Función cuadrática madre (p. 36) La función cuadrática más simple f () = ó =. Radical (p. 5) An epression made up of a radical smbol and a radicand. Radical (p. 5) Epresión compuesta por un símbolo radical un radicando. Eample 1a Radical epression (p. 5) Epression that contains a radical. Epresión radical (p. 5) Epresiones que contienen radicales. Eample 13, 15, and 1-10 are eamples of radical epressions. Radicand (p. 5) The epression under the radical sign is the radicand. Radicando (p. 5) La epresión que aparece debajo del signo radical es el radicando. Eample The radicand of the radical epression 1 + is +. 450 Visual Glossar

English Spanish Range (of a relation or function) (p. 83) The possible values of the output, or dependent variable, of a relation or function. Eample In the function = 0 0, the range is the set of all nonnegative numbers. Rate (p. ) A ratio of a to b where a and b represent quantities measured in different units. Eample Traveling 15 miles in hours results in the 15 miles rate or 6.5 mi/h. hours Rango (de una relación o función) (p. 83) El conjunto de todos los valores posibles de la salida, o variable dependiente, de una relación o función. Tasa (p. ) La relación que eiste entre a b cuando a b son cantidades medidas con distintas unidades. Rate of change (p. 100) The relationship between two quantities that are changing. The rate of change is also called slope. change in the dependent variable rate of change = change in the independent variable Ratio (p. ) A ratio is the comparison of two quantities b division. Eample Video rental for 1 da is $1.99. Video rental for das is $.99..99-1.99 rate of change = - 1 = 1.00 1 = 1 Eample 5 7 and 7 : 3 are ratios. Rational epression (p. 305) A ratio of two polnomials. The value of the variable cannot make the denominator equal to 0. Eample 3 3 +, where 0 Tasa de cambio (p. 100) La relación entre dos cantidades que cambian. La tasa de cambio se llama también pendiente. cambio en la variable dependiente tasa de cambio = cambio en la variable independiente Razón (p. ) Una razón es la comparación de dos cantidades por medio de una división. Epresión racional (p. 305) Una razón de dos polinomios. El valor de la variable no puede hacer el denominador igual a 0. Visual Glossar Rationalize the denominator (p. 9) To rationalize the denominator of an epression, rewrite it so there are no radicals in an denominator and no denominators in an radical. Eample Recursive formula (p. 51) A recursive formula defines the terms in a sequence b relating each term to the ones before it. 15 = # 15 15 15 = 15 15 = 15 5 Eample Let A(n) =.5A(n - 1) + 3A(n - ). If A(5) = 3 and A(4) = 7.5, then A(6) =.5(3) + 3(7.5) = 30. Racionalizar el denominador (p. 9) Para racionalizar el denominador de una epresión, ésta se escribe de modo que no haa radicales en ningún denominador no haa denominadores en ningún radical. Fórmula recursiva (p. 51) Una fórmula recursiva define los términos de una secuencia al relacionar cada término con los términos que lo anteceden. PearsonTEXAS.com 451

English Reflection (p. 137) A reflection flips the graph of a function across a line, such as the - or -ais. Each point on the graph of the reflected function is the same distance from the line of reflection as is the corresponding point on the graph of the original function. Eample 4 Spanish Refleión (p. 137) Una refleión voltea la gráfica de una función sobre una línea, como el eje de las o el eje de las. Cada punto de la gráfica de la función reflejada está a la misma distancia del eje de refleión que el punto correspondiente en la gráfica de la función original. O Relation (p. 83) An set of ordered pairs. Eample {(0, 0), (, 3), (, -7)} is a relation. Relación (p. 83) Cualquier conjunto de pares ordenados. Root of an equation (p. 350) A solution of an equation. Ráiz de una ecuación (p. 350) Solucion de una ecuación. Visual Glossar S Scale (p. 7) The ratio of an length in a scale drawing to the corresponding actual length. The lengths ma be in different units. Eample For a drawing in which a -in. length represents an actual length of 18 ft, the scale is 1 in. : 9 ft. Escala (p. 7) Razón de cualquier longitud de un dibujo a escala a la longitud real correspondiente. Las longitudes pueden tener diferentes unidades. Scale drawing (p. 7) An enlarged or reduced drawing similar to an actual object or place. Eample 1 4 in. 3 4 in. Dibujo a escala (p. 7) Dibujo que muestra de maor o menor tamaño un objeto o lugar dado. 1 in. Kitchen Dining Room 1 4 in. 1 1 in. 1 1 in. 45 Visual Glossar

English Spanish Scale model (p. 7) A three-dimensional model that is similar to a three-dimensional object. Eample A ship in a bottle is a scale model of a real ship. Modelo de escala (p. 7) Modelo tridimensional que es similar a un objeto tridimensional. Scatter plot (p. 144) A graph that relates two different sets of data b displaing them as ordered pairs. Eample Sales (millions of dollars) Sequence (p. 46) An ordered list of numbers that often forms a pattern. Similar figures (p. 7) Similar figures are two figures that have the same shape, but not necessaril the same size. 40 30 0 10 Diagrama de puntos (p. 144) Gráfica que muestra la relación entre dos conjuntos. Los datos de ambos conjuntos se presentan como pares ordenados. Sales vs. Advertising 0 0 10 0 30 40 50 Advertising (thousands of dollars) The scatter plot displas the amount spent on advertising (in thousands of dollars) versus product sales (in millions of dollars). Eample -4, 5, 14, 3 is a sequence. Eample D Progresión (p. 46) Lista ordenada de números que muchas veces forma un patrón. Figuras semejantes (p. 7) Dos figuras semejantes son dos figuras que tienen la misma forma pero no son necesariamente del mismo tamaño. G Visual Glossar E F H I DEF and GHI are similar. PearsonTEXAS.com 453

English Slope (p. 100) The ratio of the vertical change to the horizontal change. vertical change slope = horizontal change = - 1 -, where 1-1 0 Spanish Pendiente (p. 100) La razón del cambio vertical al cambio horizontal. pendiente = cambio vertical cambio horizontal = - 1 -, donde 1-1 0 Eample O 4 (4, ) 1 The slope of the line above is 4. Slope-intercept form (p. 115) The slope-intercept form of a linear equation is = m + b, where m is the slope of the line and b is the -intercept. Eample = 8 - Forma pendiente-intercepto (p. 115) La forma pendienteintercepto es la ecuación lineal = m + b, en la que m es la pendiente de la recta b es el punto de intersección de esa recta con el eje. Visual Glossar Solution of an inequalit (two variables) (p. 187) An ordered pair that makes the inequalit true. Eample Each ordered pair in the ellow area and on the solid red line is a solution of 3-5 10. O 4 6 8 Solución de una desigualdad (dos variables) (p. 187) Cualquier par ordenado que haga verdadera la desigualdad. Solution of a sstem of linear equations (p. 160) An ordered pair in a sstem that makes all the equations of that sstem true. Eample (, 1) is a solution of the sstem = - 3 = - 1 because the ordered pair makes both equations true. Solución de un sistema de ecuaciones lineales (p. 160) Todo par ordenado de un sistema que hace verdaderas todas las ecuaciones de ese sistema. 454 Visual Glossar

English Solution of a sstem of linear inequalities (p. 194) An ordered pair that makes all of the inequalities in the sstem true. Spanish Solución de un sistema de desigualdades lineales (p. 194) Todo par ordenado que hace verdaderas todas las desigualdades del sistema. Eample 4 O 4 64 The shaded green area shows the solution of the sstem 7-5 3 + 4 6 1. Standard form of a linear equation (p. 15) The standard form of a linear equation is A + B = C, where A, B, and C are real numbers and A and B are not both zero. Eample 6 - = 1 Standard form of a polnomial (p. 68) The form of a polnomial that places the terms in descending order b degree. Eample 15 3 + + 3 + 9 Forma normal de una ecuación lineal (p. 15) La forma normal de una ecuación lineal es A + B = C, donde A, B C son números reales, donde A B no son iguales a cero. Forma normal de un polinomio (p. 68) Cuando el grado de los términos de un polinomio disminue de izquierda a derecha, está en forma normal, o en orden descendente. Visual Glossar Standard form of a quadratic equation (p. 350) The standard form of a quadratic equation is a + b + c = 0, where a 0. Forma normal de una ecuación cuadrática (p. 350) Cuando una ecuación cuadrática se epresa de forma a + b + c = 0. Eample - + - 9 = 0 Standard form of a quadratic function (p. 36) The standard form of a quadratic function is f() = a + b + c, where a 0. Eample f() = - 5 + Forma normal de una función cuadrática (p. 36) La forma normal de una función cuadrática es f() = a + b + c, donde a 0. Stretch (p. 340) A stretch is a transformation that increases the distance between corresponding points of a graph. Estiramiento (p. 340) Un estiramiento es una transformación que aumenta la distancia entre puntos que se corresponden en una gráfica. PearsonTEXAS.com 455

English Substitution method (p. 169) A method of solving a sstem of equations b replacing one variable with an equivalent epression containing the other variable. Eample If = + 5 and + 3 = 7, then + 3( + 5) = 7. Sstem of linear equations (p. 160) Two or more linear equations using the same variables. Eample = 5 + 7 = 1-3 Sstem of linear inequalities (p. 194) Two or more linear inequalities using the same variables. Eample + 11 6 5 Spanish Método de sustitución (p. 169) Método para resolver un sistema de ecuaciones en el que se reemplaza una variable por una epresión equivalente que contenga la otra variable. Sistema de ecuaciones lineales (p. 160) Dos o más ecuaciones lineales que usen las mismas variables. Sistema de desigualdades lineales (p. 194) Dos o más desigualdades lineales que usen las mismas variables. Visual Glossar T Term of a sequence (p. 46) A term of a sequence is an number in a sequence. Transformation (p. 137) A transformation of a function = af( - h) + k is a change made to at least one of the values a, h, and k. The four tpes of transformations are dilations, reflections, rotations, and translations. Eample -4 is the first term of the sequence -4, 5, 14, 3. Eample g() = ( - 3) is a transformation of f () =. Término de una progresión (p. 46) Un término de una secuencia es cualquier número de una secuencia. Transformación (p. 137) Una transformación de una función = af( - h) + k es un cambio que se le hace a por lo menos uno de los valores a, h k. Ha cuatro tipos de transformaciones: dilataciones, refleiones, rotaciones traslaciones. Translation (p. 137) A transformation that shifts a graph horizontall, verticall, or both. Eample Translación (p. 137) Proceso de mover una gráfica horizontalmente, verticalmente o en ambos sentidos. O 4 is a translation of. 456 Visual Glossar

English Trend line (p. 144) A line on a scatter plot drawn near the points. It shows a correlation. Spanish Línea de tendencia (p. 144) Línea de un diagrama de puntos que se traza cerca de los puntos para mostrar una correlación. Eample Positive Negative Trinomial (p. 68) A polnomial of three terms. Trinomio (p. 68) Polinomio compuesto de tres términos. Eample 3 + - 5 V Verte (p. 36) The highest or lowest point on a parabola. The ais of smmetr intersects the parabola at the verte. Eample Verte form of a quadratic function (p. 346) The verte form of a quadratic function is f () = a( - h) + k, where a 0 and (h, k) is the coordinate of the verte of the function. 1 O verte Eample f () = + - 1 = ( + 1) - The verte is (-1, -). Vértice (p. 36) El punto más alto o más bajo de una parábola. El punto de intersección del eje de simetría la parábola. Forma del vértice de una función cuadrática (p. 346) La forma vértice de una función cuadrática es f () = a( - h) + k, donde a 0 (h, k) es la coordenada del vértice de la función. Visual Glossar Vertical-line test (p. 83) The vertical-line test is a method used to determine if a relation is a function or not. If a vertical line passes through a graph more than once, the graph is not the graph of a function. Eample Prueba de la recta vertical (p. 83) La prueba de recta vertical es un método que se usa para determinar si una relación es una función o no. Si una recta vertical pasa por el medio de una gráfica más de una vez, la gráfica no es una gráfica de una función. O 4 A line would pass through (3, 0) and (3, ), so the relation is not a function. PearsonTEXAS.com 457

English Vertical motion model (p. 333) The function h =-16t + vt + c models the height of a object, where h is the object s height in feet, t is the time in seconds since the object began to fall, v is the object s initial velocit, and c is the object s initial height. Spanish Modelo de movimiento vertical (p. 333) La función h =-16t + vt + c representa la altura de un objeto donde h es la altura del objeto en pies, t es el tiempo de caída en segundos, v es la velocidad inicial del objeto c es la altura inicial del objeto. X -intercept (p. 15) The -coordinate of a point where a graph crosses the -ais. Y Eample The -intercept of 3 + 4 = 1 is 4. Intercepto en (p. 15) Coordenada por donde la gráfica cruza el eje de las. Visual Glossar -intercept (p. 115) The -coordinate of a point where a graph crosses the -ais. Z Eample The -intercept of = 5 + is. Zero-Product Propert (p. 356) For all real numbers a and b, if ab = 0, then a = 0 or b = 0. Eample ( + 3) = 0 = 0 or + 3 = 0 = 0 or =-3 Intercepto en (p. 115) Coordenada por donde la gráfica cruza el eje de las. Propiedad del producto cero (p. 356) Para todos los números reales a b, si ab = 0, entonces a = 0 ó b = 0. Zero of a function (p. 350) An -intercept of the graph of a function. Cero de una función (p. 350) Intercepto de la gráfica de una función. Eample The zeros of = - 4 are {. O 458 Visual Glossar

Inde A Activit Lab Dividing Polnomials Using Algebra Tiles, 310 Modeling Equations With Variables on Both Sides, 10 Modeling Multi-Step Inequalities, 33 Solving Sstems Using Algebra Tiles, 167 168 addition of monomials, 69 of polnomials, 69 70 solving sstems of linear equations using, 176 Addition Propert of Equalit, 175 algebra tiles for area models, 77 modeling equations, 10 modeling factoring, 87 88 modeling multi-step inequalities, 33 modeling polnomial division, 310 modeling quadratic equations, 367 solving sstems, 167 168 algebraic epressions dividing, 0 multipling powers in, 10 alpha ke, of graphing calculator, 190 analsis of errors. see Error Analsis eercises of graphs, 54 and, compound inequalities containing, 40, 41 area of rectangle, 17, 80, 0 of trapezoid, 0, 354 of triangle, 17, 74 argument, defined, 13 arithmetic sequences defined, 46, 61 as functions, 48 identifing, 47 in recursive form, 51 53 writing an eplicit formula for, 48 assessment Check Your Understanding, 45, 9, 15, 199, 38, 61, 317, 378, 408 Quick Review, 45 48, 9 95, 15 155, 199 01, 38 41, 61 6, 317 31, 378 381, 408 409 TEKS Cumulative Practice, 49 51, 156 157, 0 03, 4 43, 63 65, 3 33, 38 383, 410 411 Teas End-of-Course Practice, 9, 16, 1, 6, 3, 39, 44, 58, 63, 69, 75, 8, 87, 91, 107, 11, 119, 14, 136, 143, 151, 166, 174, 180, 186, 193, 198, 09, 14, 18, 4, 8, 3, 37, 50, 55, 60, 7, 76, 81, 86, 91, 95, 300, 304, 309, 316, 33, 339, 345, 349, 355, 359, 366, 371, 377, 394, 401, 407 Topic Review, 45 48, 9 95, 15 155, 199 01, 38 41, 61 6, 317 31, 378 381, 408 409 association, 148 asmptote defined, 386 horizontal, 387 aes, 54 ais of smmetr, 36, 37, 378, 379 B base of eponent, 10 multipling powers with same, 10 best fit, line of. See line of best fit binomials defined, 68 dividing polnomials b, 31 multipling, 77 79 squaring, 8 83 break-even point, 18 C calculator. See also graphing calculator equations in slope-intercept form, 113 114 eercises that use, 336, 390 391, 391, 393 line of best fit, 147 vertical motion model, 335 causal relationships, 148 causation, 148 defined, 144 change, rate of, 100 Check Your Understanding, 45, 9, 15, 199, 38, 61, 317, 378, 408 circle area of, 17 circumference of, 17, 19 radius of, 3 circumference, 17, 19 classifing functions as linear or nonlinear, 65 lines, 133 coefficient correlation. see correlation coefficient elimination of variables using, 175 176 positive, 36 common difference, 46, 47, 48, 61 common ratio, 46, 48, 61 communication. See Reasoning eercises; writing Commutative Propert of Multiplication, 30 completing the square, 367, 381 compound inequalities containing and, 40, 41 containing or, 40, 41 defined, 40, 48 graphing, 40 44 solving, 40 44 writing, 41 4 compound interest, 395, 396, 398 compression defined, 340 graphing quadratic functions with, 341, 379 Concept Summar Choosing a Method for Solving Linear Sstems, 181 Dividing a Polnomial b a Polnomial, 311 Function Notation, 88 Graphs of Direct Variations, 108 Linear Equations, 15 Slopes of Lines, 101 Sstems of Linear Equations, 160 consistent sstems of linear equations, 160 constant of variation defined, 108 for a direct variation, 108, 153 constant ratio, 387 Inde PearsonTEXAS.com 459

Inde Constructed Response, 50 51 eercises, 157, 03, 43, 64 65, 33, 383, 411 continuous graphs, 70, 94 Converse of the Pthagorean Theorem, 33 coordinates. See -coordinates; -coordinates correlation, 144, 148 correlation coefficient, 145, 147 defined, 144 cross products defined,, 47 of a proportion, Cross Products Propert of a Proportion, cube side length of, 03 volume of, 03 cubic polnomials, factoring, 301 clinder volume of, 80, 17, 76, 307 D deca, eponential, 396, 398 399, 409 deca factor, 396, 409 decimals, solving equations containing, 6 7 degree of a monomial, 68 of a polnomial, 68, 317 denominators, rationalizing, 9, 31 dependent variables, 59, 60, 100 diagram mapping, 83 84 as problem-solving strateg. see draw a diagram difference of two squares, defined, 96 direct variation constant of variation for, 108 defined, 108 graphs of, 108 109 identifing, 108, 153 tables and, 109 110 writing equations of, 109 discrete graphs, 70, 94 discriminant defined, 37 using, 373, 375, 381 distance-rate-time problems, 100 101 Distributive Propert solving equations using, 6 solving inequalities using, 36 using to multipl binomials, 78 Dividing Powers With the Same Base, 19 divisibilit of algebraic epressions, 0 of numbers in scientific notation, 0 of polnomials, 311 313 division, of polnomials, 310 Division Propert of Eponents, 19 of Square Roots, 9, 30 domain defined, 83, 95 of a function, 89 identifing, 90 for real-world data, 404 draw a diagram, 80 E elimination, for solving linear sstems, 181 elimination method defined, 175 solving sstems of linear equations using, 175 176, 181, 184 equations. See also function(s) containing decimals, 6 7 containing fractions, 6 of direct variation, 108 110 finding slopes using, 13 of geometric relationships, 60 graphing, 11 from graphs, 116 with grouping smbols, 13 of horizontal translations, 139 identit, 13 linear. see linear equations of linear functions, 61 literal, 17 18 modeling, 10 multi-step, 4 7 with no solution, 13 of patterns, 66 of perpendicular lines, 13, 134 in point-slope form, 10, 11, 15 quadratic. see quadratic equations in slope-intercept form, 116, 15 solving using the Distributive Propert, 6 in standard form, 15 19 sstems of linear, 160 from tables, 1 of trend lines, 146 from two points, 116 with variables on both sides, 10, 11 13 of vertical translations, 139 Essential Understanding, 4, 11, 17,, 7, 34, 40, 54, 59, 64, 70, 78, 83, 88, 100, 108, 115, 10, 15, 13, 137, 144, 160, 169, 175, 181, 187, 194, 06, 10, 15, 19, 5, 9, 33, 46, 51, 56, 68, 73, 77, 8, 87, 9, 96, 301, 305, 311, 36, 333, 340, 346, 350, 356, 360, 367, 37, 386, 395, 40 estimating eercises that use. see Estimation eercises solutions of equations, 374 using substitution, 171 evaluating eponential epressions, 07 function rules, 79 ecluded value, 305 eplicit formula, defined, 46 for an arithmetic sequence, 46 eponential data analzing features of, 404 modeling, 40 404, 409 eponential deca, 395, 396, 409 graphing, 398 399 writing, 398 eponential epressions evaluating, 07 simplifing, 06 07, 1 using, 07 eponential form, converting to, 6 eponential functions defined, 386, 408 evaluating, 389 graphing, 389 460 Inde

identifing, 387, 408 writing, 388 eponential growth, 395 399, 409 eponential models, 390 eponents. See also power(s) division properties of, 15 in eponential deca models, 399, 409 in eponential growth models, 397, 409 multiplication properties of, 15 multipling, 15 17 negative, 06 07 rational, 1 simplifing epressions with, 1 zero, 06 07 epressions algebraic, 10, 0 eponential, 06 07, 10 1, 15 17, 0, 1 radical, 6, 9 31 rational, 305 307 simplifing, 9 31, 305 307 square root, 9 31 writing radical, 35 etrapolation, 145, 155 defined, 144 F factor(s) deca, 396, 409 greatest common (GCF), 74 growth, 395, 397, 409 opposite, 306 perfect-square, removing, 9 variable, removing, 30 factoring difference of two squares, 96, 98 b grouping, 301 30 monomials, 74 perfect-square trinomials, 96, 97 polnomials, 75, 301 trinomials, 87 89, 9 93, 96 98 using models, 87 88 using to solve quadratic equations, 37 factoring out common factors, 98 monomials, 74, 93 polnomials, 75 falling object model appling, 39 330 formula for, 36, 39 330 quadratic function for, 39 330 families of functions, 115 FOIL (First, Outer, Inner, Last), 78 formulas for area of a square, 16 for area of circle, 17 for area of rectangle, 17 for area of trapezoid, 0, 354 for area of triangle, 17, 74 for circumference of circle, 17, 19 for converting temperatures, 17 defined, 17, 46 for distance between points, 17, 19 for falling object model, 39 330 for perimeter of rectangle, 17, 35 for point-slope form, 10 for radius of circle, 3 slope, 100 for vertical motion, 333, 335 for volume of cube, 03 for volume of clinder, 80, 17, 76, 307 for volume of prism, 81, 307 for volume of sphere, 68 fractions, solving equations containing, 6 function notation, defined, 88 function rules evaluating, 79 graphing, 70 73 nonlinear, 73, 80 writing, 78 79, 80 function(s). See also equations; graph(s) defined, 59, 93 domain of, 83, 89 evaluating, 88 eponential, 386 391, 408 families of, 115 identifing a reasonable domain and range, 90 identifing using mapping diagrams, 83 identifing using tables, 84 identifing using verbal descriptions, 84 85 identifing using vertical line test, 84 linear parent, 115 linear vs. nonlinear, 65 modeling, 79, 117, 397 nonlinear, 64 parent, 115 quadratic. see quadratic functions range of, 83, 89 sequences as, 48 G GCF (greatest common factor), 74 geometric sequences defined, 46, 61 identifing, 47 in recursive form, 56 58 writing an eplicit formula for, 48 geometr. See also area; circle; cone; cube; perimeter; rectangle; surface area; triangle(s); volume, formulas of, 17, 19, 35, 74 golden ratio, 81 golden rectangle, 81 graph(s) analzing, 54 of boundar lines of linear inequalities, 187 188 of compound inequalities, 40 44 continuous, 70 of direct variation, 108 109 discrete, 70 of equations, 10 11 of eponential deca, 398 of eponential functions, 389, 395, 396, 408 finding slope using, 10 of function rules, 70 73 of geometric relationships, 60 of horizontal lines, 17 of horizontal translations, 139 of inequalities, 40 44, 187 190 of linear equations, 61, 64 65, 116, 117 Inde PearsonTEXAS.com 461

Inde of linear functions, 19 of linear inequalities, 187 190 matching with data table, 55 of nonlinear function rules, 73 of nonlinear functions, 64 65 of patterns, 66 quadratic, 36 330, 333 334, 350 351, 373 of a quadratic function, 333 334 of reflected functions, 138, 139 140 scatter plot, 144 shifts of. see translations sketching, 55 of solutions of sstems of linear equations, 160 163, 181 for solving linear sstems, 181 of sstems of linear equations, 160 163 of sstems of linear inequalities, 194 196 of transformations of linear functions, 137 14 of transformations of quadratic functions, 340 343 of translations, 137, 139, 340 343, 379 using point-slope form, 10 11 using slope-intercept form, 115 117 using to relate variables, 54 using to solve quadratic equations, 37 of vertical lines, 17 of vertical translations, 139 writing equations from, 116 writing linear inequalities from, 190 writing linear inequalities to, 189 writing sstems of linear inequalities from, 195 graphing calculator. See also calculator alpha ke, 190, 196 apps ke, 190, 196 CALC feature, 77, 147, 163, 335, 351, 391 correlation coefficient from, 147 eercises that use, 391, 393 finding line of best fit using, 147 graph ke, 76, 190, 196 for graphing a quadratic function, 336, 351, 36 INEQUAL, 190, 196 LinReg feature, 147 MAXIMUM feature, 335 modeling eponential data with, 390 391, 403 404 stat ke, 147 table ke, 163 tblset ke, 163 window ke, 76 Y = ke, 76, 163 zoom ke, 77, 113, 114 Graphing Functions and Solving Equations, 76 77 greatest common factor (GCF), 74 Gridded Response, eercises, 03, 33, 383, 411 ground speed, 184 grouping smbols. See also individual smbols, solving equations with, 13 growth, eponential, 395, 397, 409 growth factor, 395, 409 guess and check, 36, 18 H half-plane, 187 horizontal lines, 101, 17, 13, 188 horizontal translations, 139, 341 hpotenuse defined, 33 finding length of, 34 I identit, 11, 13, 46 inconsistent sstems of linear equations, 160 independent sstems of linear equations, 160 independent variables, 59, 7, 100 real-world, 71 inde of radical epression, 5 indirect measurement, 8 inequalit(ies). See also solving inequalities compound, 40 44 graphs of, 40 44, 194 linear. see linear inequalities multi-step, 33, 34 37 properties of. see propert(ies) with special solutions, 36 37 Triangle Inequalit Theorem, 43 with variables on both sides, 36 writing, 35, 41 4 input, 59 input value, 93 integers, in standard form, 19 intercepts. See -intercept; -intercept interest, compound, 396, 397 interpolation, 144, 145, 155 intersection, point, of sstem of linear equations, 160 K Ke Concept Asmptote of an Eponential Function = ab, 387 Ais of Smmetr of a Quadratic Function, 333 Compound Interest, 396 Continuous and Discrete Graphs, 70 The Converse of the Pthagorean Theorem, 33 Deriving the Quadratic Equation, 373 Elimination Method, 175 Equivalence of Radicals and Rational Eponents, 5 Eplicit Formula for a Geometric Sequence, 46 Eplicit Formula for an Arithmetic Sequence, 46 Eponential Deca, 396 Eponential Function, 386 Eponential Growth, 395 Factoring a Difference of Two Squares, 96 Factoring Perfect-Square Trinomials, 96 Finding Rate of Change and Slope, 100 Functions, 59 Graph of a Linear Inequalit in Two Variables, 187 Graphing Inequalities, 40 Ground Speed, 18 Line of Best Fit and Correlation Coefficient, 145 Methods for Solving a Quadratic Equation, 37 Modeling a Quadratic Epression, 367 Multipling a Monomial b a Polnomial, 73 46 Inde

Naming Polnomials, 68 Parabolas, 37 Point-Slope Form of a Linear Equation, 10 Product of a Sum and Difference, 8 Properties of Square Roots, 9 The Pthagorean Theorem, 33 Quadratic Formula, 37 Radicals, 5 Rational Epressions, 305 Recursive Definition Arithmetic Sequence, 51 Recursive Definition Geometric Sequence, 56 Reflection, 138 Reflection, Stretch, and Compression, 340 Relating Linear Factors, Solutions, and Zeros, 360 Scatter Plots, 144 Similar Figures, 7 Simplifing Radicals, 9 Slope Change, 138 The Slope Formula, 100 Slope-Intercept Form of a Linear Equation, 115 Slopes of Parallel Lines, 13 Slopes of Perpendicular Lines, 13 Solve Quadratic Equations b Graphing, 350 Square of a Binomial, 8 Standard Form of a Linear Equation, 15 Standard Form of a Quadratic Equation, 36, 350 Translation, 137, 341 Trend Lines, 145 Using an Area Model, 77 Using Rational Eponents, 10 Using Sstems of Equations to Model Problems, 181 Using the Discriminant, 373 Using the Elimination Method, 175 Verte Form of a Quadratic Equation, 346 Writing Quadratic Functions, 361 Know-Need-Plan problems, 5, 1, 4, 8, 4, 55, 61, 65, 90, 116, 16, 170, 177, 195, 07, 0, 70, 78, 87, 313, 39 330, 357, 369, 398, 40 403 L leg, 33 like terms, combining, 4 line of best fit, 145 defined, 144 finding, 147 modeling, 147 using graphing calculator to find, 147 line(s) boundar, 187 190 classifing, 133 graphing, using intercept, 16 horizontal, 101, 17, 13, 188 number line(s), 40 4 parallel, 13, 133 perpendicular, 13, 134 slope of, 101 trend, 144, 145, 146 vertical, 101, 17, 13, 188 linear equations defined, 115 graphing, 117, 19 identifing features of, 19 point-slope form of, 10, 15 slope-intercept form of, 115, 15 solving using algebra tiles, 167 168 standard form of, 15, 17 19 sstems of. see sstems of linear equations linear factors, of quadratic functions, 360, 361 linear functions defined, 59, 93 equations and, 61 graphs of, 60, 61, 64 65, 116 117, 19 multiplication b a constant, 140 141 nonlinear functions vs., 64 65 patterns and, 59 61 rate of change of, 10 slope change, 138 tables and, 60, 61, 19 transformations of, 137 14 linear inequalities boundar lines of, 187 190 defined, 187, 01 graphing, 188 190 solving. see solving inequalities sstems of. see sstems of linear inequalities writing from graphs, 190 writing to graphs, 189 linear parent functions, 115 linear regression, 145 literal equation defined, 17, 46 with onl variables, 18 rewriting, 17 18 M manipulatives, 5. See also algebra tiles mapping diagrams, 83 mathematical modeling with algebra tiles, 10, 33, 167 168, 367 area model, 8 83 of division of polnomials, 310 of equations, 10 eponential data, 40 404, 409 of eponential deca, 399 of eponential growth, 397 eponential models, 390 for factoring, 87 88 factoring a polnomial, 75 falling objects, 39 330 of a function, 79, 117, 397 of inequalities, 33 line of best fit, 147 of products of binomials, 77 of products of polnomials, 77 scale, 9 30 to solve equations with variables on both sides, 10 to solve multi-step inequalities, 33 to solve quadratic equations, 367, 374 trend line, 145 using diagrams, 5, 1, 78, 79, 80, 83 using equations, 8, 9 30, 66, 79 using graphs, 116, 117, 10, 10 11, 134, 160 using polnomials, 69 70 using standard form of linear equation, 18 19 Inde PearsonTEXAS.com 463

Inde using sstems of equations, 18 using tables, 101, 1, 145 for vertical motion, 333, 335 maimum value (of parabola), 36, 37, 379 measurement, indirect, 8 mental math, 5 Mental Math, problems, 8, 84 minimum value (of parabola), 36, 37, 379 models. See mathematical modeling monomial adding and subtracting, 69 defined, 68, 317 dividing a polnomial b, 311 factoring out, 74, 93 Multiple Choice eercises, 49 50, 96 97, 156 157, 0, 4 43, 63 64, 3 33, 367 368, 38 383, 410 411 problems, 8, 36, 55, 116, 134, 176, 190, 16, 1, 30, 35, 73, 79, 313, 39, 343, 357 multiplication of binomials, 77 79 of eponents, 15 of numbers in scientific notation, 11 1 of polnomials of degree one, 73 of powers, 10 1 properties of. see propert(ies) solving sstems of linear equations using, 177 178 of a trinomial and a binomial, 79 Multiplication Propert of Eponents, 10 Multipling Powers With the Same Base, 10 N negative correlation, defined, 144 negative eponents, 06 negative slope, 101 no correlation, defined, 144 nonlinear function rules graphing, 73 writing, 67, 80 nonlinear functions defined, 64, 93 graphs of, 64, 65 vs. linear functions, 64 patterns and, 64 66 representing, 66 rules describing, 67 nth root, defined, 5 null set. See empt set number line(s) for graphing compound inequalities, 40 linear inequalities in one variable graphed as, 188 number sense, 58 defined, 56 numbers dividing, in scientific notation, 0 integers, 19 multipling, in scientific notation, 11 1 O opposite factors, 306 opposite reciprocals, 13, 134, 154 or, compound inequalities containing, 41 ordering, terms, 313 output, 59 output value, 93 P parabolas ais of smmetr of, 36, 37 comparing widths of, 38 defined, 36, 378 maimum point of, 36, 37 minimum point of, 36, 37 in quadratic graphs, 37 39 smmetr of, 36, 37 verte of, 36, 37 parallel lines, 13, 133, 154 parent functions, 115, 36, 37 patterns. See also sequences equations representing, 66 and geometric relationships, 60 graphing, 66 and linear functions, 59 61 and nonlinear functions, 64 67 representing, 66 in sequences, 47 tables showing, 66 percent increase, 141 perfect-square trinomial, 96, 97 defined, 96 perimeter of heagon, 11 of rectangle, 17, 35, 0 perpendicular lines, 13, 134, 154 points equations from two, 116 finding slope using, 103 formula for distance between, 17, 19 of intersection of lines, 160 point-slope form of linear equations, 10 1, 17 18, 133, 153 polgon, 03 polnomial(s) adding, 69 70 classifing, 69 defined, 68, 317 dividing, 310, 311 313 dividing with a zero coefficient, 313 factoring out, 75 modeling with, 69 70 multipling, 77 naming, 68 standard form of, 68 subtracting, 70 positive coefficients, in multi-step inequalities, 36 positive correlation, 144 positive number(s), in nonlinear functions, 73 positive slope, 101 power(s). See also eponents in algebraic epressions, 10 1 multipling, 10 1, 15 17 raising a power to, 15 raising a product to, 15 17 raising a quotient to, 19, 1 with same base, 10 1 simplifing, 06 464 Inde

Practice and Application Eercises, 7 9, 14 16, 19 1, 4 6, 30 3, 37 39, 4 44, 56 58, 6 63, 67 69, 73 75, 80 8, 85 87, 90 91, 104 107, 110 11, 118 119, 1 14, 19 131, 135 136, 14 143, 148 150, 164 166, 17 174, 178 180, 184 186, 191 193, 196 198, 08 09, 13 14, 17 18, 1 3, 7 8, 31 3, 36 37, 49 50, 53 55, 58 60, 71 7, 75 76, 80 81, 84 85, 90 91, 94 95, 99 300, 303 304, 307 309, 314 315, 330 33, 337 339, 344 345, 348 349, 353 354, 358 359, 364 366, 370 371, 376 377, 391 394, 399 401, 405 407 principal square root, defined, 5 prism, 81, 30 problem-solving strategies draw a diagram, 80, 79 find a pattern, 60, 66, 47 guess and check, 36, 18 make a table, 60, 65, 71, 161, 78, 88 89 make an organized list, 88 89 solve a simpler problem, 4, 6, 67, 07, 11, 9, 79 tr, check, revise, 1 work backward, 4 write an equation, 5, 61, 79, 18, 313, 368, 1103 products cross, of powers with same base, 10 1 radical epressions involving, 30 simplifing, 15 16 of a sum and a difference, 84 propert(ies) Addition Propert of Equalit, 175 Commutative Propert of Multiplication, 30 Cross Products Propert of a Proportion, Distributive Propert, 6, 36, 78 Dividing Powers With the Same Base, 19 Division Propert of Eponents, 19 Division Propert of Square Roots, 9, 30 Multiplication Propert, 3 Multiplication Propert of Eponents, 15 Multiplication Propert of Square Roots, 9 Multipling Powers With the Same Base, 10 Raising a Power to a Power, 15 Raising a Product to a Power, 15 Raising a Quotient to a Power, 19 Subtraction Propert of Equalit, 175 Zero and Negative Eponents, 06 Zero-Product Propert, 356, 380 proportions defined, multi-step, 3 in similar figures, 7 solving, 6 solving using Cross Products Propert, 3 solving using Multiplication Propert, 3 using to find side lengths, 8 using to interpret scale drawings, 9 using to solve problems, 4 Pthagorean Theorem converse of, 33 defined, 33 using, 33 35, 41 Q quadratic equations choosing method for solving, 375 choosing reasonable solution, 35 defined, 350 modeling, 367 roots of, 350, 35 solutions of, 380 solving b completing the square, 367 369 solving b factoring, 356 358 solving b graphing, 351 solving using square roots, 35 standard form of, 350, 357 Quadratic Formula, 373 defined, 37 deriving, 373 using, 37 375, 381 quadratic functions defined, 36, 378 graphs of, 36 330, 333 334, 340 343, 350 351, 360 363, 373 identifing ke attributes, 37 parent function, 36, 37 roots of, 36 standard form of, 36, 363 verte form of, 346 348 zero of, 350, 361, 380 zero product propert of, 356 quadratic graphs, 36 330, 333 334, 350 351, 360 363, 373 quadratic parent function, 36, 37 quadratic regression, 333 Quick Review, 45 48, 9 95, 15 155, 199 01, 38 41, 61 6, 317 31, 378 381, 408 409 quotients radical epressions involving, 30 31 raising to a power, 19, 1 R radical epressions, 41 defined, 5 multipling, 30 simplifing, 9 31 simplifing b multipling, 9 using, 6 writing, 35 radical form, converting to, 6 radicals defined, 5 simplifing, 9 31 radicands, defined, 5 radius, of circle, 3 Raising a Power to a Power, 15 Raising a Product to a Power, 15 Raising a Quotient to a Power, 19 range defined, 83, 95 of a function, 89 of function, 83, 38, 389 identifing, 83, 90 reasonable, 389 Inde PearsonTEXAS.com 465

Inde rate(s). See also distance-rate-time problems of change, 100 104, 15 defined, ratio(s), defined, rational eponents and radicals, 5 using, 10 rational epression(s) defined, 305, 30 simplifing, 305 307 using, 307 rationalize a denominator, 31 defined, 9 reasonableness, defined, 87, 360 reciprocals, opposite, 13, 134 rectangle area of, 17 perimeter of, 17, 35 recursive definition, 51, 6 recursive formula defined, 51 writing, 5, 53, 57 reflections defined, 137 graphing, 138, 139 140, 340, 379 Relate-Define-Write problems, 5, 1, 8, 35, 78, 79, 18, 16, 176, 399, 403 relation(s) causal, 148 defined, 83, 95 and domain, 83 and range, 83 Review. See Topic Review right triangles defined, 33 hpotenuse of, 33, 34 identifing, 35 legs of, 33, 34 Pthagorean Theorem and, 33 35 rise, 100 root of an equation, 350 roots. See nth root; square roots rules describing nonlinear functions, 67 function, writing, 78 79 writing, 67, 80 run, 100 S SAT test prep. See assessment; Gridded Response; Multiple Choice scale, 9 scale drawings, 9 scale models, 9 30 scatter plots defined, 144, 155 making, 145 trends in, 144 scientific calculator. See calculator; graphing calculator scientific notation dividing numbers in, 0 multipling numbers in, 11 1 raising a number to a power in, 17 sequences defined, 46, 61 etending, 47 terms of, 46 using, 58 writing an eplicit formula for, 48 set(s), data. see data signs. See negative numbers; positive number(s) similar figures appling similarit to proportions, 8 defined, 7 finding lengths of sides of, 8 problems involving, 7 3 simplifing algebraic epressions, 06, 1, 15 16, 1 eponential epressions, 06 07, 1, 15 16, 1 fractions within radicals, 30 powers, 06 07, 1, 15 16, 1 radical epressions, 9 31 rational epressions, 305 307 slope change in, 138 defined, 100, 15 finding, 100 104, 13, 133 formula for, 100 graphing, 138 graphs of, 100 104, 113 114 of horizontal and vertical lines, 103 of a line, 101 negative, 101 of parallel lines, 13 of perpendicular lines, 13 positive, 101 rate of change as, 100 slope-intercept form, 115 117, 15, 133, 153 solution of a sstem of linear inequalities, defined, 194 solution of an inequalit, defined, 187 solve a simpler problem, 4, 6, 67, 07, 11, 9, 79 solving equations. See also equations; quadratic equations containing decimals, 6 7 containing fractions, 6 with infinitel man solutions, 17 linear, b graphing, 160 163 linear, choosing method of, 181 linear, using elimination method, 175 176, 184 linear, using substitution method, 169 17, 181 multi-step, 4 7 with one variable, 390 391 using elimination method, 181 using graphs, 181 using substitution, 170 solving inequalities compound, 40 44 linear, 187 multi-step, 34 37 with no solution, 37 Solving Sstems Using Algebra Tiles, 167 168 sphere(s), volume of, 68, 85 square roots. See also radicals defined, 5 Division Propert of, 9, 30 Multiplication Propert of, 9 solving quadratic equations using, 35 using to solve quadratic equations, 37 466 Inde

square(s) of a binomial, 83 completing, 367 difference of two, 96, 98 perfect, 9, 96, 97 perfect-square trinomials, 96, 97 standard form, 153 of linear equations, 15 of polnomials, 68 of quadratic equations, 350, 374, 380 of quadratic functions, 36, 363 using as a model, 18 19 writing linear equations in, 17 18 STEM, 14, 19, 0, 1, 6, 9, 31, 37, 43, 44, 55, 6, 75, 90, 109, 111, 11, 117, 13, 134, 146, 161, 184, 186, 07, 08, 09, 11, 13, 17, 18,, 3, 6, 7, 36, 37, 76, 85, 90, 94, 97, 303, 308, 315, 33, 354, 358, 399, 401 strateg, defined, 87, 360 stretch defined, 340 graphing quadratic functions with, 341, 379 substitution, for solving linear sstems, 181 substitution method defined, 169 solving for a variable using, 170 solving sstems of linear equations using, 181 for verifing an estimate, 171 subtraction of monomials, 69 of polnomials, 70 properties of. see propert(ies) solving sstems of linear equations using, 176 Subtraction Propert of Equalit, 175 surface area, of prism, 1 sstems of linear equations choosing a method for solving, 181 consistent, 160 defined, 160 dependent, 160 finding break-even points using, 18 graphing, 160 163, 199 inconsistent, 160 independent, 160 with infinitel man solutions, 16, 178 with no solution, 16, 17 with one solution, 16 solving. see solving equations using to solve real-world problems, 170 171 writing, 161 sstems of linear inequalities defined, 194, 01 graphing, 194 196 writing, from graphs, 195 T table ke, of graphing calculator, 163 tables direct variation and, 109 110 of direct variation variables, 109 110 finding rate of change using, 101 of geometric relationships, 60 for graphing quadratic functions, 38 matching with graphs, 55 patterns shown using, 66 representing linear functions, 60, 19 writing linear inequalities from, 190 Take Note, 11, 17,, 7, 40, 59, 64, 70, 88, 100, 101, 108, 115, 10, 15, 13, 137, 138, 144, 145, 160, 175, 181, 18, 187, 06, 10, 15, 19, 5, 9, 33, 46, 51, 56, 68, 73, 77, 8, 96, 301, 305, 311, 36, 37, 333, 340, 341, 346, 350, 356, 360, 361, 367, 37, 373, 386, 395, 396 Technolog Lab Graphing Functions and Solving Equations, 76 77 Investigating = m + b, 113 114 TEKS Cumulative Practice, 49 51, 156 157, 0 03, 4 43, 63 65, 3 33, 38 383, 410 411 temperature, formula for converting, 17 term of a sequence, defined, 46 terms of arithmetic sequences, 46 like, 4 of recursive arithmetic sequences, 5 of recursive geometric sequences, 57 58 reordering in polnomial division, 313 Teas End-of-Course Practice, 9, 16, 1, 6, 3, 39, 44, 58, 63, 69, 75, 8, 87, 91, 107, 11, 119, 14, 136, 143, 151, 166, 174, 180, 186, 193, 198, 09, 14, 18, 4, 8, 3, 37, 50, 55, 60, 7, 76, 81, 86, 91, 95, 300, 304, 309, 316, 33, 339, 345, 349, 355, 359, 366, 371, 377, 394, 401, 407 theorems Pthagorean, 33 Triangle Inequalit, 43 Think-Write problems, 103, 11, 16, 6, 74, 84, 93, 98, 306, 347 348, 35, 375 Three-Act Math, 3, 5 53, 98 99, 158 159, 04 05, 44 45, 66 67, 34 35, 384 385 time. See distance-rate-time problems Topic Review, 45 48, 9 95, 15 155, 199 01, 38 41, 61 6, 317 31, 378 381, 408 409 transformations defined, 137, 154 describing a combination of, 343 of linear functions, 137 14 of quadratic functions, 343, 363, 379 translations defined, 137, 154 graphing, 137, 139, 340 343, 379 horizontal, 139, 341 vertical, 139, 341 trend. See correlation trend line, 145, 146 defined, 144, 155 Triangle Inequalit Theorem, 43 triangle(s) area of, 17, 74 inequalit in, 43 isosceles right, 74 length of side of, 37 Inde PearsonTEXAS.com 467

Inde trinomials defined, 68 factoring, 87 89, 9 93, 96 98 of the form a + b + c, 9 93 of the form + b + c, 87 89 multipling a binomial b, 79 perfect-square, 96, 97 in rational epressions, 306 with two variables, 89 V variable(s) on both sides of an equation, 11 13 dependent, 59, 100 in direct variation equations, 108 110 eliminating, 175, 178 in equations, 10, 11 13 independent, 59, 60, 71, 7, 100 in linear equations, 115 in linear inequalities, 187 190 verte form, 379 defined, 346 interpreting, 346 using, 347 writing a quadratic function in, 347 verte of a parabola, 36, 37, 378 vertical line test, 84 defined, 83 vertical lines, 104, 17, 13, 188 vertical motion model, 333, 335 vertical translations, 139, 341 viable solution, 183 Vocabular, 4, 11, 17,, 7, 34, 40, 54, 59, 64, 70, 78, 83, 88, 100, 108, 115, 10, 15, 13, 137, 144, 160, 169, 175, 181, 187, 194, 06, 10, 15, 19, 5, 9, 33, 46, 51, 56, 68, 73, 77, 8, 87, 9, 96, 301, 305, 311, 36, 333, 340, 346, 350, 356, 360, 367, 37, 386, 395, 40 volume of cube, 03 of clinder, 80, 76, 307 formulas for, 69, 80, 76, 85 of prism, 80, 307 of sphere, 68, 85 W write an equation, 5, 1, 61, 79, 18, 368 writing direct variation equations, 110 direct variation from tables, 110 equations from graphs, 116 equations from two points, 116 equations in point-slope form, 10, 11, 15, 133 equations in slope-intercept form, 116, 15, 133 equations in standard form, 15, 17 18 equations of direct variation, 109 equations of parallel lines, 133 equations of perpendicular lines, 13, 134 equations of trend lines, 146 eplicit formulas, 53 eplicit formulas for sequences, 48 eponential deca function, 398 eponential functions, 388 function rules, 78 79, 80 inequalities, 35 linear inequalities to graphs, 189 quadratic equations, 360 363 quadratic functions in verte form, 349 radical epressions, 35 recursive formulas, 5, 53, 57 Relate-Define-Write problems, 403 rule describing nonlinear functions, 67 sstem of linear equations, 161 sstem of linear inequalities from graphs, 195 Think-Write problems, 103, 11, 16, 6, 74, 84, 93, 98, 306, 347 348, 35, 375 X -intercept, 15 16, 13 Y -intercept, 115, 116, 117, 15 16, 153, 160 Z zero as coefficient, 313 as eponent, 06 of quadratic functions, 380 slope of horizontal line as, 101 as substitute for - or -intercept, 15 zero of a function, 361 defined, 350 Zero-Product Propert, 356, 380 468 Inde

Acknowledgments Cover Design Tom White / 9 Surf Studios Brian Reardon and Jamee Farinella Photographs Photo locators denoted as follows: Top (T), Center (C), Bottom (B), Left (L), Right (R), Background (Bkgd) Cover Gerald French/Corbis. 00 (Bkgrd) RTimages/Fotolia, (C) CRISSY PASCUAL/UT/ZUMA Press, Inc./Alam; 00 Reuters/Corbis; 09 (BC) Ingram Publishing/ Superstock, (BR) The Franklin Institute, Philadelphia, P.A., (CL) Medi-Mation Ltd/Science Source; 05 Maridav/Fotolia; 07 (CL) istockphoto, (C) Ian O Lear/Dorling Kindersle, (CR) Talor S. Kenned/National Geographic Stock; 098 Antenna/fStop/Alam; 109 (BCR) NASA/AP Photo, (CR) GSFC/NASA, (TCR) Friedrich Saurer/ Science Source; 117 (CR) Tobias Bernhard/Corbis, (R) David Joner/ istockphoto; 146 Eric Baccega/age fotostock/alam; 158 Jeff Greenberg/PhotoEdit, Inc.; 161 (BL) Ilian Animal/Alam, (BR) James Carmichael Jr./Photoshot; 04 steven r. hendricks/shutterstock; 08 Kevin Schafer/Photoshot; 14 GeoStills/Alam; 7 bunwit/fotolia; 8 (TCR) fotopak/fotolia, (TR) Aaron Amat/Fotolia; 34 Rob Belknap/ istockphoto; 36 Geoffre Morgan/Alam; 37 Laure Neish/ istockphoto; 44 Jacek Chabraszewski/Fotolia; 54 Keantian/Fotolia; 66 Seeberg/Caro/Alam; 75 (BR) Paulo Fridman/Corbis, (CR) brt PHOTO/Alam; 80 Henr Wilson/Photoshot; 97 Brandon Alms/ Shutterstock; 315 iofoto/fotolia; 34 Larr W. Smith/EPA/Newscom; 338 Julie Lubick/Shutterstock; 347 Brian Bevan/Alam; 357 Sl/Fotolia; 384 Tomas del amo/alam; 389 Nigel Cattlin/Alam; 39 Biophoto Associates/Science Source; 399 Seigo Yamamura/Aflo/Gett Images. Acknowledgments PearsonTEXAS.com 469