2. What is the problem asking you to determine? A function that gives the surface area of a box with dimensions 4 in. 3 4 in. 3 h in.

Transcription

1 - Think About a Plan Relations and Functions Geometr Suppose ou have a bo with a -in. square base and variable height h. The surface area of this bo is a function of its height. Write a function to represent the surface area. Evaluate the function for h. in. Understanding the Problem. The width of the bo is u inches. The length of the bo is u inches. The height of the bo is u h inches.. What is the problem asking ou to determine? A function that gives the surface area of a bo with dimensions in. in. h in., and the surface area when h. in. Planning the Solution. What is the area of the top of the bo? What is the area of the bottom of the bo? in. ; in.. What is the total area of the top and the bottom of the bo? in.. What is the area of each side of the bo? h in.. What is the total area of the sides of the bo? h in. Getting an Answer. Write a function to represent the surface area of the bo. s(h) h. Evaluate our function for h. inches. in. Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

2 - Practice Form K Relations and Functions A motion detector tracks an egg as it drops from ft above the ground. The table shows the height at various times.. Represent the data using each of the following: a. a mapping diagram b. ordered pairs (, ), (.,.), (.,.), (.,.), (.,.) c. a graph on the coordinate plane a. Domain Range c o..... What are the domain and range of this relation? Domain:,.,.,.,.; Range:,.,.,.,. Time (seconds)..... Height (feet).... Determine whether each relation is a function.. Domain Range. (, ), (, ), (, ), (, ), (, ) es es Use the vertical-line test to determine whether each graph represents a function.. O. O. O es es no Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

3 - Practice (continued) Form K Relations and Functions Evaluate each function for the given value of.. f () for. f () for. f () for. f () for. f () for. f () for. Open-Ended Write a function rule that produces an output of for an input of.. Answers ma var. Sample: f(). A cable compan charges a monthl fee of $. for cable service. There is an additional monthl fee of $ for each premium channel. George has cable service with premium channels. Write and evaluate a function to find the monthl cost of George s cable service. Variables ma var. Sample: f().; $.. Mr. Renolds is a car salesman. He makes a salar of $, a ear. He also earns a commission of of his total sales for the ear. This ear, Mr. Renolds has a sales total of $,. Write and evaluate a function to find Mr. Renolds s total earnings for the ear. Variables ma var. Sample: f(),; $,. Kinetic energ is the energ of an object in motion. The formula K mv is used to calculate kinetic energ. The variable m is the object s mass, and v is its velocit. Calculate the kinetic energ of a kilogram object traveling at meters per second. Your answer will be in Joules.. Joules Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

4 - Standardized Test Prep Relations and Functions Multiple Choice For Eercises, choose the correct letter.. Which relations are functions? I. A III. O O II. IV. O O II and III I and II III and IV I and IV. Which point could not be part of a function that includes (, ), (, ), (, ), (, ), and (, )? G (, ) (, ) (, ) (, ). For the function f (), which of the following is f ()?. What is the domain of the relation given b the ordered pairs? (, ), (, ), (, ), (, ), (, ) {,,, } {,,, } {,,, } {,,, } Short Response. A phone store emploee earns a salar of $ per week plus % commission on her weekl sales. a. What function rule models the emploee s weekl earnings? b. If the emploee earned $ in a week, what was the amount of her sales for that week? [] a. f (). b. $ [] incorrect function rule OR incorrect sales amount [] no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved. G C

5 - Think About a Plan Direct Variation Sports The number of rotations of a biccle wheel varies directl with the number of pedal strokes. Suppose that in the biccle s lowest gear, pedal strokes move the cclist about in. In the same gear, how man pedal strokes are needed to move ft? Know. The number of rotations of a biccle wheel varies directl with the number of pedal strokes.. pedal strokes move the cclist in. There are in. in a foot. Need. To solve the problem I need to: Find the constant of variation b solving for k in d kp, convert ft to inches, and then use the constant of variation to find the number of pedal strokes needed to move ft. Plan. Write an equation of direct variation to model the situation. Find the constant of variation. k ; k.. Substitute for one variable and the constant of variation in the equation of direct variation.. p. What does the solution mean? About pedal strokes are needed to move the cclist ft.. Is the solution reasonable? Eplain. Yes; ft is in., which is between and times in.; pedal strokes is between and times pedal strokes. Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

6 - Practice Form K Direct Variation For each function, determine whether varies directl with. If so, find the constant of variation and write the function rule. To start, write ratios of output to input.. es; k,. no. es; k, ; ; Determine whether varies directl with. If so, find the constant of the variation.... es; k no no For Eercises, varies directl with.. If when, find when.. If when, find when.. If when, find when.. If when, find when.. The length of an object s shadow varies directl with the height of the object. A ft tree casts a ft shadow. a. Write a function rule and determine the constant of variation. ; k b. What length shadow would a ft tree cast? ft c. What height tree would cast a ft long shadow?. ft Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

7 - Practice (continued) Form K Direct Variation Write and graph a direct variation that passes through each point.. (, ). (, ). (, ) For each function, determine whether varies directl with. If so, find the constant of variation and write the function rule. To start, write ratios of output to input.... ; ; es, k, es, k, no. Error Analsis Suppose varies directl with. If when, what is when? You sa that and our friend sas. Who is correct? What mistake was made? Your friend is correct; ou reversed our - and -values when setting up the direct variation or multiplied when ou should have divided. You incorrectl used k instead of k.. Suppose ou drive a car mi on a tank of gas. The tank holds gallons. The number of miles traveled varies directl with the number of gallons of gas ou use. a. Write an equation that relates miles traveled to gallons of gas used. Let the number of gallons of gas used and the number of miles driven. b. Last ear ou drove, mi. Approimatel how man gallons of gas did ou use? about gallons Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

8 - Standardized Test Prep Direct Variation Multiple Choice For Eercises, choose the correct letter.. If varies directl with and is when is, which of the following represents this situation? B. Which function best represents the relationship between the quantities in the table? H. If varies directl with and is when is, what is when is? B. Which equation of direct variation has (, ) as a solution? I. Which equation does NOT represent a direct variation? C Short Response. You can download a MB file in seconds. The time t it takes to download a file varies directl with the size s of the file. Write an equation of direct variation to represent the situation. How long will it take ou to download a MB file? [] t s;. s [] incorrect equation OR incorrect time [] no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

9 - Think About a Plan Linear Functions and Slope-Intercept Form The equation d t represents our distance (in miles) from home d for each minute of our walk t. a. If ou graphed this equation, what would the slope represent? Eplain. b. Are ou walking towards or awa from our home? Eplain.. What does d represent? our distance from home in miles. What does t represent? the number of minutes ou spend walking. Is the equation in slope-intercept form? If not, write the equation in slope-intercept form. no; d t. What units make sense for the slope? Eplain. mi/min; slope is the ratio of the change in distance to the change in time (in minutes), and it is reasonable to walk mi in min, or mi/hr.. What does the slope represent? Eplain. The constant rate b which our distance from home changes; ou walk at a rate of mi per min towards home.. Is our distance from home increasing or decreasing? decreasing Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

10 - Practice Form K Linear Functions and Slope-Intercept Form Find the slope of the line through each pair of points. To start, substitute (, ) and (, ) into the slope formula.. (, ) and (, ). (, ) and (, ). (, ) and (, ) m m m m Write an equation for each line.. m and the -intercept is. m and the -intercept is.. O O Write each equation in slope-intercept form. Then find the slope and -intercept of each line. To start, isolate the -term on one side of the equation.... ; m ; -intercept is ; m ; -intercept is ; m ; -intercept is Graph each equation.... O O O Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

11 - Practice (continued) Form K Linear Functions and Slope-Intercept Form. The equation models the number of pages ou finished reading in our tetbook after ou read for hours this week. a. Write this equation in slope-intercept form. the speed at which ou b. If ou graph this equation, what would the slope represent? read our tetbook, in c. Reasoning In this situation, what does the point (, ) represent? pages per hour the number of pages,, ou finished reading after reading for hour this week Graph each equation. Find the slope and -intercept.... m, m, (, -intercept: -intercept:, ) O O O (, ). Multiple Choice For the equation, which has value? B ( ) the -intercept the -intercept the slope the origin m, -intercept:. Error Analsis For the graph at the right, a classmate said the slope is. What mistake did she make? What is the correct slope? She used the run over the rise to determine the slope instead of the rise over the run. The correct slope is. O. Writing Eplain how the graph of a line with a negative slope differs from the graph of a line with a positive slope. The graph of a line with a negative slope falls from left to right. The graph of a line with a positive slope rises from left to right. Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

12 - Standardized Test Prep Linear Functions and Slope-Intercept Form Multiple Choice For Eercises, choose the correct letter.. For the linear equation, which of the following has a value of? A the slope the -intercept the -intercept the origin. What is true about the line that passes through the points (, ) and (, )? It is horizontal. It is vertical. H It rises from left to right.. What is the slope-intercept form of? It falls from left to right. B. What is the -intercept of the graph of? H. Which of the following is a graph of? C O O O O Short Response Write the equation in slope-intercept form. What are the slope and the -intercept?. [] ; ; [] incorrect equation OR incorrect slope OR incorrect -intercept [] no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

13 - Think About a Plan More About Linear Equations a. Write the point-slope form of the line that passes through A(, ) and B(, ). Use point A in the equation. b. Write the point-slope form of the same line using point B in the equation. c. Rewrite each equation in standard form. What do ou notice?. What is the point-slope form of an equation of a line? m( ). What is the standard form of an equation of a line? A B C. What is the slope formula? Use the slope formula to find m. m (). Use point A to write the point-slope form. z z z z ( ). Write the point-slope form of the equation using point A in standard form.. Use point B to write the point-slope form. z z z z ( ). Write the point-slope form of the equation using point B in standard form.. Compare the standard form of the equation using point A with the standard form of the equation using point B. The are the same. Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

14 - Practice Form K More About Linear Equations Write an equation of each line.. slope ; through (, ). slope ; through (, ). slope ; through (, ). slope ; through (, ) Write in point-slope form an equation of the line through each pair of points. To start, substitute values for (, ) and (, ) into the slope formula.. (, ) and (, ). (, ) and (, ). Q, R and Q, R m ( ) or ( ) Q R or ( ) Q R or Q R Write an equation of each line in standard form with integer coefficients. To start, multipl each side b the least common denominator of all fractional coefficients... () Q R.. Reasoning The line ( ) contains point (a, ). Find a. Show our work. Since the line contains the point (a, ), a and must make the equation true. Substituting these values gives (a ), which can then be solved for a: a ; a; a; a. Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

15 - Practice (continued) Form K More About Linear Equations Find the intercepts and graph each line.... O O O (, ); (, ). Rosa must read pages of a book for English class. It will take Rosa about minutes to complete her reading. Draw a graph and write an equation to represent the situation. Number of Pages (, ); (, ) (, ); (, ). O Number of Minutes. According to the information in Eercise, how long will it take Rosa to read pages? minutes Write an equation in slope-intercept form for each line.. the line parallel to through (, ). the line perpendicular to through (, ) Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

16 - Standardized Test Prep More About Linear Equations Multiple Choice For Eercises, choose the correct letter.. For the linear equation, which of the following has value? B the slope the -intercept the -intercept the origin. Which represents the slope of a line that is parallel to a line with a slope of? H. Which equation represents a line through (, ) that is perpendicular to? A. Which equation represents a line through (, ) with a slope of? F ( ) ( ) ( ) ( ). Which of the following equations is shown in the graph? ( ) ( ) ( ) ( ) Short Response. The line is graphed on a coordinate plane. A second line is drawn on the same plane with a slope of and -intercept (, ). Write the equation of the second line. Describe the relationship between these two graphs. D O [] ; the lines intersect at the same -intercept of Q, R [] incorrect equation OR incorrect description [] no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

17 - Think About a Plan Using Linear Models Data Analsis The table shows population and licensed driver statistics from a recent ear. a. Make a scatter plot. b. Draw a trend line. c. The population of Michigan was approimatel million that ear. About how man licensed drivers lived in Michigan that ear? d. Writing Is the correlation between population and number of licensed drivers strong or weak? Eplain. Licensed Drivers Population State (millions) Arkansas. Illinois. Kansas. Massachusetts. Pennslvania. Teas. Number of Drivers (millions) Know. The independent variable should be population, in millions.. Points to plot: (.,.), (.,.), (.,.), (.,.), (.,.), (.,.) Need. To solve the problems, I need to Plan. Make the scatter plot.. Draw a trend line on the scatter plot. make a scatter plot; draw a trend line; use the trend line to find the number of licensed drivers if the population is million; find the strength of the correlation.. How do ou find the equation of the trend line? Write the equation. Use two data points to write the point-slope form of the equation. Answers ma var. Sample:.. Licensed Drivers (millions) Population and Number of Licensed Drivers Population (millions). About how man licensed drivers lived in Michigan that ear? about. million. What is correlation? Is the correlation between population and licensed drivers strong or weak? Eplain. Correlation is the strength of the relationship, or how close the data points are to the trend line; the correlation is strong; the points fall ver close to the trend line. Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

18 - Practice Form K Using Linear Models Make a scatter plot and describe the correlation. To start, plot the points.. (, ), (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ), (, ) strong positive correlation Write the equation of a trend line, if possible.. (, ), (, ), (, ), (, ), (, ) Answers ma var. Sample:.. weak negative correlation. To begin, make a scatter plot and let correspond to. Life Epectanc for People Born in Various Years Year Life Epectanc SOURCE: National Center for Health Statistics Answers ma var. Sample:... The table below shows the average dail energ requirements for male children and adolescents. Dail Energ Requirements for Males Age (ears) Energ needed (calories) SOURCE: Go Figure: The Numbers You Need for Everda Life a. Use a calculator to find the line of best fit... b. Use our linear model to predict how man calories a -ear old needs per da. about calories c. Use our linear model to predict the age of a male who needs calories per da. ears old d. Reasoning Do ou think this model also applies to adult males? Eplain. No; energ requirements for adult males do not continue increasing, so the linear model will not appl to adults. Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

19 - Practice (continued) Form K Using Linear Models. A woman is considering buing a car. She researches prices for various ears of the same model of car. The table below shows the data from her research. Car Prices b Model Year Model Year Prices $ $ $ $ $, a. Use a calculator to find the line of best fit. Let the number of ears since... b. Use our linear model to predict how much a model should cost. $,. c. Error Analsis She predicts that a model costs $. Does this seem reasonable? Wh or wh not? A model should cost more than a model, but $ is less than $, so this is not reasonable. The linear model gives a prediction of $,. for a model of this car, which is a reasonable estimate. Consider each situation and predict the tpe of correlation ou might find. Do ou think that changes in the first quantit caused the changes in the second quantit?. a person s weight and the size of clothing the wear strong positive correlation; as a person s weight increases, so does the size of clothing that person wears. The first quantit causes the change in the second quantit.. the number of rooms in a person s home and the number of books a person owns These two things do not have an correlation with each other.. the length of time a candle has been burning and the height of the candle strong negative correlation; the longer a candle burns, the shorter the candle will become. The first quantit causes the change in the second quantit. For each situation, find a linear model and use it to make a prediction.. A -mi cab ride costs $.. A -mi cab ride costs $.. How much does a.-mi cab ride cost?..; $.. There are blades of grass in in. of lawn. There are blades of grass in in. of the same lawn. How man blades of grass are in in. of lawn? Answers ma var. Sample:..; about blades of grass. An empt -gal water jug weighs. lb. With c of water inside, the jug weighs. lb. Predict the weight of the jug with c of water inside...;. lb Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

20 Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved. Name Class Date Gridded Response Solve each eercise and enter our answer in the grid provided. Use the table and the scatter plot for Eercises. Ependitures (billions of dollars) Year.... SOURCE: The World Almanac and Book of Facts, U.S. Health Ependitures Drug and Other Medical Nondurables. What is the -intercept of the trend line if the trend line using a slope of. and the point (,.)?. During what ear did the U.S. spend $ billion in health ependitures?. Using the points for and, what is the slope of the trend line? Round to the nearest hundredth.. Use the equation.., where is. About how man billion dollars would the U.S. have spent on health ependitures in the ear, rounded to the nearest tenth? Standardized Test Prep Using Linear Models Answers Ependitures (billions of dollars) Number of ears since...

21 - Think About a Plan Families of Functions Suppose ou are plaing with a o-o during a school talent show. You make a graph of the o-o s distance from the auditorium floor during the show. If someone started to take a video of our o-o routine when ou were introduced, seconds before ou actuall started, what transformation would ou have to make to our graph to match the video? Understanding the Problem. What is the problem asking ou to determine? The transformation needed to change a graph of the o-o routine to represent the graph of a video of the routine that started s earlier.. How is this problem related to problems about parent functions? This problem is like an problem that changes a parent function to another function through transformations. Planning the Solution. What quantit is represented b the independent ais in our graph? time. What quantit is represented b the dependent ais in our graph? The o-o s height above the floor of the auditorium. If ou graph the routine that ou perform, what is represented on the independent ais in our graph? The dependent ais? The time period of the routine; the height above the auditorium floor. If ou graph the routine that ou see on the video, what is represented on the independent ais in our graph? The dependent ais? The time period of the recording; the height above the auditorium floor Getting an Answer. What transformation would ou make to our graph to match a graph of the video? Translate it right s. Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

22 - Practice Form K Families of Functions How is each function related to its parent function? Graph the function b translating the parent function.. The graph of is the. ( ) The graph of ( ) is graph of translated up units. the graph of translated left units. ( ) O... Q R. ( ) The graph of. is the graph of translated down. units. The graph of Q R is the of translated right unit. Make a table of values for f () after each given translation.. units down. units up. units down Write an equation for each horizontal translation of f ()... units right. unit left. units right f() (.) f() Q R f() ( ) Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

23 - Practice (continued) Form K Families of Functions Describe the transformation that changes the parent function f () to g().. g().(). g(). g() () vertical compression b reflection in the -ais vertical stretch b a a factor of. factor of Write an equation for each transformation of f ().. a vertical compression b a factor of and a reflection in the -ais g(). a vertical stretch b a factor of and a vertical translation up units g(). a vertical stretch b a factor of. and a reflection in the -ais g(). Writing Eplain how to tell the difference between a stretch and a compression without graphing. If the factor is greater than, then the transformation is a stretch. If the factor is greater than zero and less than one, then the transformation is a compression. Graph each pair of functions on the same coordinate plane. Describe the transformation that changes f () to g().. f () g() g() f() g() is a translation of f() up units. f () g() g() f() g() is a reflection of f () in the -ais and a translation down units OR a reflection in the -ais and a translation up units Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

24 - Standardized Test Prep Families of Functions Multiple Choice For Eercises, choose the correct letter.. Which of the following is the graph of reflected in the -ais and verticall compressed b a factor of? D O O O. The graph of is translated units down. Which point is on the new graph? I (, ) (, ) (, ) (, ). The graph of f () is reflected in the -ais and translated units right. Which is the equation of the new graph? C f ( ) f ( ) f ( ) f ( ). Which equation represents the vertical translation of f () up units? f () f ( ) f () f ( ). Which equation represents the horizontal translation of to the left units? A H Short Response. How will a vertical compression of the parent function change the graph of the function? Write a new equation that represents this transformation. [] A vertical compression decreases the slope, making the line less steep. Equations ma var, but should be of the form a where R a R. [] incorrect eplanation OR incorrect equation [] no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

25 - Think About a Plan Absolute Value Functions and Graphs Graph u u. List the verte and the - and -intercepts, if an. Understanding the Problem. What is the problem asking ou to determine? the graph of», an absolute value function, and its verte and - and -intercepts. What is the parent function for the function u u?» Planning the Solution. What do ou know about the function u u? The graph requires multiple transformations of the parent function.. Graph the parent function.. What transformations do ou need to appl to the parent function to graph this function? Translate right units; stretch verticall b a factor of ; translate up unit O Getting an Answer. What is the verte of the function? (, ). What are the - and -intercepts of the function? no -intercepts; -intercept: (, ). Graph the function. O Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

26 - Practice Form K Absolute Value Functions and Graphs Make a table of values for each equation. Then graph the equation.. u u O. u u. u u. u u O O O Graph each function. Then describe the transformation from the parent function f ()».. u u. P P. u u O vertical stretch b a factor of b a factor of / Without graphing, identif the verte, ais of smmetr, and transformations from the parent function f ()».. u u. u u. verte (, ), ais of smmetr ; stretched b a factor of and translated left unit reflection in the -ais and vertical compression verte (, ), ais of smmetr ; translated right units and up units O vertical stretch b a factor of P P verte (, ), ais of smmetr ; reflected in the -ais and compressed b a factor of and translated down units Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

27 - Practice (continued) Form K Absolute Value Functions and Graphs Write an absolute value equation for each graph.... O O»»» O. Error Analsis For the graph to the right, ou said the absolute value equation is u u. Your friend said the equation is u u. Which one of ou is correct? What mistake did the other person make? You are correct. Your friend reversed the signs when writing the transformed absolute value equation. O Graph each absolute value equation.. u u. u u. P P O O. Writing Eplain how to find the verte of u u. To write the equation in verte form a» h k, first factor the absolute value epression as»( ). Since is a positive constant,»( )»»( ). Now, the equation can be written as», from which it can be seen that the verte (h, k) is (, ). O Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

28 - Standardized Test Prep Absolute Value Functions and Graphs Multiple Choice For Eercises, choose the correct letter.. Which equation has the graph shown at the right? u u u u u u D u u. Which statement about the graph of the function u u is true? I the verte is at (, ) the verte is at (, ) the verte is at (, ) the verte is at (, ). The graph of which equation is the graph of f () u u reflected in the -ais, translated units left, verticall compressed b a factor of, and translated up units? B u u u u u u u u Etended Response. Determine the parent function of u u. Describe the graph of u u as three transformations of the parent function. Then graph the parent function and each translation. [] f ()» ; the graph of u u is the parent function f ()» translated units left, reflected in the -ais and translated down unit. [] correct parent function, but with one error in describing and graphing the transformations [] incorrect parent function OR multiple errors in describing and graphing the transformations [] incorrect parent function AND incorrect description of all transformations OR missing graph [] no answers given O Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

29 - Think About a Plan Two-Variable Inequalities The graph at the right relates the amount of gas in the tank of our car to the distance ou can drive. a. Describe the domain for this situation. b. Wh does the graph stop? c. Wh is onl the first quadrant shown? d. Reasoning Would ever point in the solution region be a solution? e. Write an inequalit for the graph. f. What does the coefficient of represent? Distance (mi) Miles Traveled Gas in Tank (gallons). What is the domain of a function? all possible values of the independent variable. What is the domain for this situation? K K, where is the number of gallons of gas in the tank. What is the upper bound of the domain in this situation?. Wh does the graph stop? The tank can onl hold gal of gas; the graph stops at gal.. What do ou know about the - and -values of points in the first quadrant? Both - and -values are positive.. Wh is onl the first quadrant shown? Both the quantit of gas in the tank and the miles driven are alwas nonnegative.. Would ever point in the solution region be a solution? Eplain. Yes; ever point represents a quantit of gas and a possible number of miles ou could drive using that quantit of gas.. Write an equation for the boundar line in the graph.. Write an inequalit for the graph. K ( is the no. of gallons of gas in the tank). What does the coefficient of represent? the gas mileage (mi/gal) of the car Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

30 - Practice Form K Two-Variable Inequalities Graph each inequalit. To start, graph the boundar line..,. $., O O. You want to bu some CDs that cost $ each and some DVDs that cost $ each. You have $ to spend. a. Write an inequalit to represent the situation, where is the number of CDs ou bu and is the number of DVDs. K b. Graph the inequalit. This is a real situation and ou cannot have negative c. Reasoning Wh did the graph in b onl include quadrant I? quantities of CDs and DVDs. d. Reasoning Can ou bu CDs and DVDs? Eplain. No; those coordinates are outside the feasible region and when ou substitute these values of and into the inequalit, the statement is not true. O Graph each absolute value inequalit. To start, graph the boundar line.. $ u u. # u u., u u O O O. Open-Ended Write an absolute value inequalit for which the boundar is dashed and the shaded region is above the boundar. Answers ma var. Sample: an inequalit of the form S a» h k; where a S Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

31 - Practice (continued) Form K Two-Variable Inequalities Write an inequalit for each graph. The equation for the boundar line is given... u u. u u O O O S K» R» Graph each inequalit on a coordinate plane.... $. u u $ O O O. The graph at the right relates the number of hours ou spend sleeping to the number of hours ou spend on the computer each weekend. a. Describe the domain for this situation. K K b. Write an inequalit for the graph. K c. What is the least amount of time ou can spend sleeping? What is the most amount of time ou can spend on the computer? hours; hours d. Reasoning Wh does this graph onl go to on both the -and -aes? There are onl hours in a weekend. O (, ) (, ) Prentice Hall Foundations Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.

32 - Standardized Test Prep Two-Variable Inequalities Multiple Choice For Eercises, choose the correct letter.. Which graph best represents the solution of the inequalit #? O O D. Which ordered pair is a solution of.? (, ) (, ) (, ) (, ) G. Which ordered pair is not a solution of $ P P? B (, ) (, ) (, ) (, ). The graph of which absolute value inequalit has its verte at (, )? F. u u.u u. u u.u u Short Response. Transportation The high school band is epecting to take at least students to a regional band competition. The school rents some passenger vans that can transport students. Other students, in groups of, will need to ride in personal vehicles driven b parents. a. Write an inequalit that shows all the possible combinations of vans and cars that could be used to drive students to the competition. b. Eplain in words or show work for how ou determined the inequalit. [] a. L where represents the number of vans and represents the number of cars (OR equivalent inequalit) b. Because each van holds students, the total number of students riding in vans is. Because each car holds students, the total number of students riding in cars is. The total number of student passengers must be at least, so the sum of and is greater than or equal to. (OR equivalent eplanation) [] incorrect inequalit OR incorrect eplanation [] incorrect answers and no work shown OR no answers given Prentice Hall Algebra Teaching Resources Copright b Pearson Education, Inc., or its affiliates. All Rights Reserved.