Skills Practice Skills Practice for Lesson 1.1

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1 Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabular Define each term in our own words.. function A function is a relation that maps each value of the independent variable to exactl one value of the dependent variable.. linear function A linear function is a function that has a constant rate of change and a graph that is a non-vertical straight line.. independent variable An independent variable is a variable assigned to an independent quantit.. dependent variable A dependent variable is a variable assigned to a dependent quantit. 009 Carnegie Learning, Inc. 5. variable A variable is a letter or smbol that represents a quantit. Problem Set Determine the independent quantit and the dependent quantit in each example. 6. A car is traveling at a rate of sixt miles per hour for several hours. independent quantit: time in hours dependent quantit: distance in miles Chapter Skills Practice

2 7. Sharon is growing at a rate of two inches per ear. independent quantit: time in ears dependent quantit: height in inches 8. The area of a square floor is the product of the length of two of its sides. independent quantit: side length of floor dependent quantit: area of floor 9. The perimeter of a square is the sum of the length of all four of its sides. independent quantit: side length of square dependent quantit: perimeter of square 0. The length of a video file in minutes relates to the size of the file in btes. independent quantit: length of a video file in minutes dependent quantit: size of the file in btes. The total weight of a bag of apples in pounds relates to the number of apples in the bag. independent quantit: number of apples dependent quantit: total weight of bag in pounds Define a variable to represent each of the quantities. Then write an equation that shows the relationship between the two variables.. A runner travels miles per hour. Write an equation to show the relationship between the total distance the runner travels and the time. Let t represent the amount of time in hours. Let d represent the distance the runner travels in miles. d t 009 Carnegie Learning, Inc.. Each DVD at an electronics store costs $.50. Write an equation to show the relationship between the total cost when purchasing DVDs and the number of DVDs. Let n represent the number of DVDs purchased. Let c represent the total cost of buing n DVDs in dollars. c.5n Chapter Skills Practice

3 Name Date. To make one solar panel, a compan uses two kilograms of silicon. The compan has 00 kilograms of silicon. Write an equation to show the relationship between the amount of silicon remaining and the number of solar panels made. Let s represent the amount of silicon remaining in kilograms. Let n represent the number of solar panels made. s 00 n 5. A bowling ball compan uses seven pounds of resin to make one seven-pound bowling ball. The have a total of 90 pounds of resin. Write an equation to show the relationship between the amount of resin remaining and the number of seven-pound bowling balls made. Let r represent the amount of resin remaining in pounds. Let b represent the number of bowling balls made. r 90 7b 6. Julia opens a bank account and deposits $500 into the account. Each month, she deposits $50 into the account. Write an equation to show the relationship between the total amount of mone in her bank account and the number of months since she opened the account. Let m represent the number of months since Julia opened the account. Let d represent the total amount in the account in dollars. 009 Carnegie Learning, Inc. d 50m A water tower contains 5,000 gallons of water. Each week, 500 gallons of water are used and 000 gallons of water are added. Write an equation to show the relationship between the total amount of water remaining in the water tower and the number of weeks that have elapsed. Let w represent the number of weeks that have elapsed. Let g represent the amount of water remaining in the water tower in gallons. g 5, w Chapter Skills Practice

4 Graph each linear function. 8. x 9. x = x 0 x = x + 0 x 0. x. x = x + = x 0 x 0 x. x 5 = x 5. x Carnegie Learning, Inc. 0 x 0 x = x 7 Chapter Skills Practice

5 Name Date Use the given information to answer each question.. The distance, d, in miles that a plane travels can be modeled b the equation d 550t, where t represents the time in hours. If the plane travels for 7 hours, how far will it go? d 550t d 550(7) d 850 The plane will travel 850 miles in 7 hours. 5. The distance, d, in feet that a fl travels can be modeled b the equation d 5t, where t represents the time in seconds. If the fl travels for 0 seconds, how far will it have gone? d 5t d 5(0) d 50 The fl will travel 50 feet in 0 seconds. 009 Carnegie Learning, Inc. 6. The equation w,000,000 0m shows the amount of water, w, in gallons remaining in a water tower, where m represents the number of minutes that have passed. When will there be 750,000 gallons of water in the water tower? w 0m,000, ,000 0m,000,000 50,000 0m,500 m After,500 minutes, or 08 hours and 0 minutes, there will be 750,000 gallons of water in the tower. Chapter Skills Practice 5

6 7. The equation a t shows the amount of mone, a, in dollars remaining in a bank account where t represents the time in weeks. When will the balance in the account be $000? a 50t t t 5 t After 5 weeks, the balance in the bank account will be $ A ticket seller s weekl earning, s, in dollars can be modeled b the equation s 0.0t 50, where t represents the number of tickets he sells. How man tickets will the ticket seller have to sell to make $0 that week? s 0.0t t t 900 t The ticket seller will have to sell 900 tickets that week to make $0. 9. The total number of computers, c, that a compan can manufacture can be modeled b the equation c s 50, where s represents the number of 50 screws that the need to order. How man screws will the need to order so that the can manufacture 55 computers? c 50 s s s,750 s 009 Carnegie Learning, Inc. The compan needs to order,750 screws to manufacture 55 computers. 6 Chapter Skills Practice

7 Skills Practice Skills Practice for Lesson. Name Date Calculating Answers Solving Linear Equations and Linear Inequalities in One Variable Vocabular Write the term that best completes each statement.. The solution of an inequalit can be graphed on a(n) number line.. Adding, subtracting, multipling, and distributing are all examples of simplifications that can be used to solve an equation.. Addition, subtraction, multiplication, and division are the four basic transformations that can be applied to both sides of a linear equation to solve the equation.. A(n) inequalit is a statement that compares two expressions. Problem Set Indicate which transformation(s) are needed to solve each equation. 5. x 6. x Add to both sides. Subtract from both sides. 009 Carnegie Learning, Inc. 7. x 8. x 7 Divide both sides b. Multipl both sides b. 9. x 8 0. First, subtract from both sides. x 5 5 First, add 5 to both sides. Then, divide both sides b. Then, multipl both sides b. Chapter Skills Practice 7

8 S olve each equation.. x 0. x x 0 x x 7 x. x 6 0. x 9 7 x x x 6 x 8 x 6 x 8 x 8 x 6 5. x 6. x x x x x 6 ( x ) ( ) ( x ) (6) x 7. x 8. 5 x 8 x 8 x 5 x 8 x 5 x ( x ) ( ) 5 ( 5 x ) 5( ) x x x 6 x 60 x 60 x Carnegie Learning, Inc. 8 Chapter Skills Practice

9 Name Date 9. x 5 5 x 0. x x 9 x x x 5 5 x x x x x 9 x x 5x 5 5 x 9 5x x 9 5x 0 x 5x x S olve each inequalit. Graph the solution on a number line.. x 8. x 5 7 x 8 x x 6 x x 6 x x x x. x x x x 6 x Carnegie Learning, Inc. x 6 x x 9 x x 5 6. x x 5 x x 8 x 7 x 8 x 7 x Chapter Skills Practice 9

10 7. ( x ) 5 8. (x 5) ( x ) 5 x 5 ( x 5) x 5 x 5 5 x 5 5 x 9 x ( 9 ) (x) 9 6 x x x 0. x 0 x x 0 x x ( x ) () ( x ) () 5 0 x x 5 x x Carnegie Learning, Inc. 0 Chapter Skills Practice

11 Skills Practice Skills Practice for Lesson. Name Date Running a 0K Slope-Intercept Form of Linear Functions Vocabular Determine each of the following for the linear function x 6.. slope. -intercept. slope-intercept form. x-intercept x x Problem Set Identif the slope of each linear function. 5. x 6. x The slope is. The slope is. 009 Carnegie Learning, Inc. 7. x 8. 5 x 5 The slope is. 5 The slope is. Identif the -intercept of each linear function. 9. 5x 0. x The -intercept is. The -intercept is.. x. x The -intercept is. The -intercept is. Chapter Skills Practice

12 Write a linear equation in slope-intercept form for each situation.. Louise opens a bank account and deposits $50. Ever month she deposits $50 into her account. Write an equation to represent the amount she has in her account after x months. 50x 50. Erin opens a bank account and deposits $50. Ever month she withdraws $5 from her account. Write an equation to represent the amount she has in her account after x months. 5x A computer is downloading a 00-megabte program file. It downloads the program at a rate of 5 megabtes per minute. Write an equation to represent the number of megabtes left to download after x minutes. 5x Marco has 0 gigabtes of computer programs on his computer. Ever month he adds.5 gigabtes of programs to his computer. Write an equation to represent the number of gigabtes of programs he has on his computer after x months..5x 0 Calculate the slope and -intercept for each function. 7. A linear function passes through the points (0, 0) and (, 8). The -intercept is 0. m 8 0 x x 0 8 The slope is. 8. A linear function passes through the points (0, 0) and (, 7). The -intercept is 0. m x x The slope is Carnegie Learning, Inc. Chapter Skills Practice

13 Name Date 9. A linear function passes through the points (, 9) and (, 5). m x x 5 9 ( ) 7 The slope is 7. mx b 5 7 () b 5 7 b b 7 7 The -intercept is A linear function passes through the points ( 5, ) and (, 0). m 0 x x ( ) ( 5) 8 The slope is. mx b 009 Carnegie Learning, Inc. 0 () b 0 9 b b The -intercept is.. A linear function passes through the points (, 0) and (, ). m x x 0 The slope is. mx b 0 () b 0 6 b b 6 The -intercept is 6. Chapter Skills Practice

14 . A linear function passes through the points (, 6) and (, 0). m x x 0 ( 6) ( ) 6 The slope is. mx b 0 ( ) b 0 b b The -intercept is. Graph each linear function using its slope and -intercept.. x. x Slope -intercept Slope -intercept = x + 0 x 0 x = x 009 Carnegie Learning, Inc. Chapter Skills Practice

15 Name Date 5. x 6. x Slope Slope -intercept -intercept = x = x + 0 x 0 x Slope 0 Slope 0 -intercept -intercept = 009 Carnegie Learning, Inc. 0 x 0 x = Chapter Skills Practice 5

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17 Skills Practice Skills Practice for Lesson. Name Date Pump It Up Standard Form of Linear Functions Vocabular Give an example of each ke term.. standard form of a linear equation x. slope-intercept form of a linear equation x Problem Set For each linear equation written in standard form, calculate the x- and -intercepts. Use the intercepts to graph the equation.. x. x x 0 0 x 0 0 x x x-intercept ; -intercept x-intercept ; -intercept 009 Carnegie Learning, Inc. (0, ) (, 0) 0 x (, 0) 0 x (0, ) Chapter Skills Practice 7

18 5. x 6 6. x x 6 6 x x x-intercept ; -intercept x-intercept ; -intercept (0, ) (0, ) (, 0) 0 x 0 (, 0) x 7. x x x x x 5 x x-intercept 5; -intercept x-intercept ; -intercept ( 5, 0) 5 0 (, 0) x (, 0) 0 x 009 Carnegie Learning, Inc. (0, ) 8 Chapter Skills Practice

19 Name Date 9. x 0. x 5 x x 5 5 x x 5 5 x-intercept 5 ; -intercept x-intercept 5; -intercept 0 x (, 0) ( 5, 0) x (0, 5 ) (0, ) Rewrite each linear equation in slope-intercept form.. x. x x x 009 Carnegie Learning, Inc.. x 5. x x 5 x x 5 5. x 6. 5x 5 x 5x 5 x 5 x 5 7. x 8. x 5 0 x 5 x 0 x 5 x Chapter Skills Practice 9

20 Rewrite each linear equation in standard form. 9. x 0. x 5 x x 5. x. x x x x x. 5 x 6. 5 x 5 9 5x 5 x 5 5x x Carnegie Learning, Inc. 0 Chapter Skills Practice

21 Skills Practice Skills Practice for Lesson.5 Name Date Shifts and Flips Basic Functions and Linear Transformations Vocabular Write the term that best completes each statement.. A function undergoes a(n) dilation when it is stretched or shrunk.. A(n) line of reflection is a line in which a function is flipped so that it mirrors itself.. A(n) reflection is a transformation in which a function is flipped over a given line.. The function x is the basic function of the function x. Problem Set Indicate the algebraic transformation which was performed on the basic function to result in each transformed function. 5. x 6. x Add. Subtract. 009 Carnegie Learning, Inc. 7. x 8. 5 x Multipl b. Multipl b 5. Indicate the graphical transformation(s) which were performed on the basic function to result in each transformed function. 9. x Move the graph down units. 0. x Move the graph up unit.. x Dilate b a factor of, then shift up units.. x Dilate b a factor of, reflect about the x-axis, and shift down units. Chapter Skills Practice

22 . x Dilate b a factor of, reflect about the x-axis, and shift up units.. 5 x Dilate b a factor of 5, and shift up units. Graph each set of equations on the same grid. Compare the graphs of the lines. Then determine whether the graphs of the lines are parallel, perpendicular, or neither. 5. x and x 6. x and x = x + = x + = x 0 x 0 x = x The first graph is shifted two units up from the second graph. The lines are parallel. The second graph is twice as steep as the first graph. The lines are neither parallel nor perpendicular. 009 Carnegie Learning, Inc. Chapter Skills Practice

23 Name Date 7. x and x 8. x and x = x + = x + 0 x = x 0 x = x + The first graph is reflected about the x-axis and shifted down units from the second graph. The lines are perpendicular. The second graph is times as steep as the first graph, reflected about the x-axis, and shifted up unit from the first graph. The lines are perpendicular. 9. x and x 0. x and x = x + = x Carnegie Learning, Inc. 0 x = x The first graph is shifted down units from the second graph. The lines are parallel. 0 x = x The second graph is twice as steep as the first graph and shifted down units from the first graph. The lines are neither parallel nor perpendicular. Chapter Skills Practice

24 . x and 5x. x and x 5 = 5x 0 x = 5 x = x 0 x = x The second graph is 5 times as steep as the first graph and reflected about the x-axis. The lines are perpendicular. The first graph is reflected about the x-axis. The lines are perpendicular.. x and x.. 0 and = = x + 0 x = x The first graph is shifted up units from the second graph. The lines are parallel. 0 x = 0 The second graph is shifted up units from the first graph. The lines are parallel. 009 Carnegie Learning, Inc. Chapter Skills Practice

25 Skills Practice Skills Practice for Lesson.6 Name Date Inventor and Sand Determining the Equations of Linear Functions Vocabular Identif the similarities and differences between each pair of ke terms.. point-slope form and two-point form Both are forms of linear equations that use a point on a line and the slope of a line. If ou divide both sides of a linear function in point-slope form b x x, then the linear function will be in two-point form.. parallel lines and perpendicular lines Parallel lines never intersect and their slopes are the same. Perpendicular lines intersect and their slopes are negative reciprocals. Problem Set Determine the slope-intercept form of the equation of each line.. Slope and -intercept. Slope and -intercept Carnegie Learning, Inc. x x 0 5. Slope and -intercept 6. Slope and -intercept x x Determine the slope-intercept form of the equation of each line. 7. Slope 5 and the line passes 8. Slope 0 and the line passes through the point (, ) through the point (, 5) 5( x ) 5 0( x ) 5x 0 5 0x 0 5x 0x 5 Chapter Skills Practice 5

26 9. Slope 7 and the line passes through 0. Slope and the line passes the point (, ) through the point (5, 6) ( ) 7( x ) ( 6) ( x 5) 7x 7 6 x 5 7x x 9 Determine the slope-intercept form of the equation of the line passing through each pair of points.. (, ) and (5, ). (, 6) and (5, 8) m 5 m ( x 5) x 5 x 7 8 ( x 5) x 0 8 x. (, 5) and (, ). (, 7) and (5, ) m 5 ( ) 8 6 m ( 7) 5 5 ( x ) x 5 x 8 5 x 8 x 7 5. (0, ) and (, ) 6. (, ) and (, ) m m Carnegie Learning, Inc. 6 Chapter Skills Practice

27 Name Date Determine the slope-intercept form of the equation of each line, given the equation of a line parallel to the line and a point on the line. 7. x, (, ) 8. 5x 6, (, 5) () b 5 5() b b 5 5 b x 0 b 5x 0 9. x, (, 6) 0. x, (, ) 6 ( ) b () b 6 b b b 8 b x x 8. x, (6, 5). x 0, (, ) 5 (6) b () b 5 b 6 b b b x x 009 Carnegie Learning, Inc. Determine the slope-intercept form of the equation of each line, given the equation of a line perpendicular to the line and a point on the line.. x, (, ). x, (, ) m m ( x ) x x m m ( x ) x x 5 Chapter Skills Practice 7

28 5. x, (, ) 6. x 9, ( 5, ) m m m m ( ) ( x ) ( x ( 5)) x 9 x 0 x 7 x 7. x 6, (0, ) 5 8. x, (, 0) m m 5 m m 5( x 0) 5x 0 ( x ) x 009 Carnegie Learning, Inc. 8 Chapter Skills Practice

29 Skills Practice Skills Practice for Lesson.7 Name Date Absolutel! Absolute Value in Equations and Inequalities in One and Two Variables Vocabular Match each example with the term that describes it.. x a. absolute value expression b. absolute value equation. x b. absolute value equation a. absolute value expression. x 5 c. absolute value inequalit c. absolute value inequalit. x 5 8 d. compound inequalit d. compound inequalit 009 Carnegie Learning, Inc. Problem Set Solve each equation. 5. x 6. x 5 x x 5 x x 5 x 7, x, 7 7. x 7 8. x 0 x 5 x x 5 x x 5 x x, 6 x 7, Chapter Skills Practice 9

30 9. x 8 0. x x 8 x x 8 x x x x 5, x, 5 Graph each equation.. x. x = x + = x 0 x 0 x. x 6. x 6 0 x = x 6 = x x 009 Carnegie Learning, Inc. 0 Chapter Skills Practice

31 Name Date 5. x 6. x 8 = x 0 x 0 5 x = x 8 Solve each inequalit and graph its solution on a number line. 7. x 8. x x or x x or x x 9 or x 5 x or x 0 x or x 5 x 6 or x x 5 0. x Carnegie Learning, Inc. x 5 or x 5 x 0 or x 0 x 8 or x x 6 or x x 8 or x x. x x or x x or x x 6 or x x or x x 9 or x x or x Chapter Skills Practice

32 Graph each inequalit.. x. x > x < x + 0 x 0 x 5. x 6 6. x < x 6 > x + 0 x 0 x 7. x 6 8. x 009 Carnegie Learning, Inc. 0 5 x < x x > x Chapter Skills Practice

33 Skills Practice Skills Practice for Lesson.8 Name Date Inverses and Pieces Functional Notation, Inverses, and Piecewise Functions Vocabular Give an example of each term.. relation For ever number, double it and add three.. domain All the x values such that x is greater than or equal to two.. range All the values such that is less than negative three.. function x 009 Carnegie Learning, Inc. 5. inverse operations Folding a piece of paper and unfolding a piece of paper are inverse operations. Adding and subtracting are inverse operations. 6. functional notation f( x) x 7. identit function f( x) x 8. inverse functions f( x) x, f ( x) x Chapter Skills Practice

34 9. composition of functions f(g( x)) 0. piecewise function f( x) x x 0 x x 0 Problem Set Rewrite each linear function using functional notation.. x. x f( x) x f( x) x. x 6. x f( x) x f( x) x 6 Calculate the value of each function for the given values of the independent variable. 5. f( x) x, calculate f( ) and f() f( ) ; f() 6. f( x) x, calculate f( ) and f() f( ) ; f() 7. k( x) x 5, calculate k( 5) and k(8) k( 5) 0; k(8) 9 8. k( x) x, calculate k(0) and k(6) k(0) ; k(6) 9. g( x) x x, calculate g( ) and g() 009 Carnegie Learning, Inc. g( ) ; g() 8 0. g( x) x, calculate g( ) and g() g( ) ; g() 9 Chapter Skills Practice

35 Name Date Determine the inverse of each function.. f( x) x. f( x) x f ( x) x f ( x) x. g( x) 5x. g( x) x g ( x) x 5 g ( x) x 5. h( x).x. 6. h( x).5x 5.6 h ( x) 0x h ( x) 0x 56 5 For the functions f( x) x and g( x) x, calculate each composition. 7. f(g()) 8. g(f()) f(g()) f( 6) 6 g(f()) g() () 9. g(f( )) 0. f(g( )) g(f( )) g( ) ( ) f(g( )) f(9) 9. f(f()). g(g()) f(f()) f() 6 g(g()) g( 6) ( 6) Carnegie Learning, Inc. Graph each piecewise function.. f( x) x x x x 5 0 x. f( x) x x x x 0 x Chapter Skills Practice 5

36 5. g( x) x x x x x x 0 x 6. g( x) x x x x x x x 6 8 Write a piecewise function to model each situation. 7. A rental car compan charges $0.5 per mile for the first 00 miles. After 00 miles the charge $0.0 per mile. Let c(m) be the cost for driving m miles. c(m) 0.5m m 00 0.m m A laundromat charges $.5 per pound of laundr for the first 0 pounds needed to be cleaned. After 0 pounds the charge $0.75 per pound. Let c(l) be the cost for cleaning l pounds of laundr. c(l).5l l l l 0 9. A movie theatre charges $5.00 per ticket for people between the ages of 0 and 5 ears. The charge $7.50 per ticket for people above the age of 5. Let c(a) be the cost of a movie if a person s age is a ears. c(a) 5 a a Carnegie Learning, Inc. 0. A garage will inflate biccle tires that are smaller than 0 inches in diameter for $.50. The charge $.5 to inflate biccle tires that are 0 inches or larger. Let c(d ) be the cost to inflate a biccle tire that has a diameter of d inches. c(d).5 d 0.5 d 0 6 Chapter Skills Practice

37 Name Date. A home-and-garden store charges $0.5 for a cubic ard of gravel if ou bu 0 cubic ards or less. The charge $9.50 for a cubic ard of gravel if ou bu between 0 and 5 cubic ards. The charge $8.75 for a cubic ard of gravel if ou bu 5 cubic ards or more. Let c( ) be the cost of cubic ards of gravel c( ) An airline charges different ticket prices based on the number of miles a plane travels. If a plane travels less than 500 miles, an airline will charge $0.85 per mile. If a plane travels 500 miles to 500 miles, the charge $0.70 per mile. If a plane travels more than 500 miles, the charge $0.55 per mile. Let c(m) be the cost to fl m miles. 0.85m m 500 c(m) 0.7m 500 m m m Carnegie Learning, Inc. Chapter Skills Practice 7

38 009 Carnegie Learning, Inc. 8 Chapter Skills Practice