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1 Chapter Famil and Communit Involvement (English) Famil and Communit Involvement (Spanish)... 7 Section Section Section Section Section Section Section Cumulative Review Algebra 1 Copright Big Ideas Learning, LLC

2 Name Date Chapter Graphing Linear Functions Dear Famil, Have ou ever thought about how much ou might weigh on another planet? Or wh ou would weigh a different amount on another planet? What is gravit? How does gravit affect our weight on Earth? Is mass different from weight? If so, how is it different? Use the Internet to research these questions before considering how our weight would change if ou visited another planet. Here is an activit for ou to complete as a famil to determine how much ou would weigh on different planets and on the moon. Upon completing the chart below, graph the information in a coordinate plane. Given the equation M = 0.17 E, where M represents an object s weight on the moon and E is an object s weight on Earth, determine how much each member of our famil would weigh on the moon. Insert the weight of each member of our famil in the chart below, from least to greatest. E ( ) M( ) Is our weight on Earth more or less than our weight on the moon? Now determine our famil's weight on Mercur and Jupiter using the equations below. Complete a chart similar to the one above for each planet. Use a calculator if needed. Graph our weight on the moon, Earth, Mercur, and Jupiter in a coordinate plane, using a different color for each. The equation for Mercur is = 0.8. The equation for Jupiter is =.5. Using our graph, which planet would ou weigh the most on? The least? How can ou tell? How about our pet? How much would he or she weigh on the moon? Consider using the equations above to determine the weight of other items if the were on the other planets. Enjo eploring outer space together! Copright Big Ideas Learning, LLC Algebra 1 71

3 Nombre Fecha Capítulo Hacer gráficas de funciones lineales Estimada familia: Alguna vez han pensado cuánto pesarían aproimadamente en otro planeta? O por qué tendrían otro peso en otro planeta? Qué es la gravedad? De qué manera la gravedad afecta sus pesos en la Tierra? La masa es diferente al peso? Si lo es, en qué se diferencia? Consulten en Internet para investigar sobre estas preguntas antes de considerar cómo cambiarían sus pesos si visitaran otro planeta. A continuación, encontrarán una actividad para que completen en familia para determinar cuánto pesarían en distintos planetas en la Luna. Después de completar la siguiente tabla, hagan una gráfica de la información en un plano de coordenadas. Dada la ecuación M = 0.17 E, donde M representa el peso de un objeto en la Luna E es el peso de un objeto en la Tierra, determinen cuánto pesaría cada integrante de la familia en la Luna. Ingresen el peso de cada integrante de su familia en la siguiente tabla, de menor a maor. E ( ) M( ) Su peso en la Tierra es maor o menor que su peso en la Luna? Ahora determinen el peso de su familia en Mercurio Júpiter usando las siguientes ecuaciones. Completen una tabla similar a la tabla de arriba para cada planeta. Usen una calculadora si la necesitan. Hagan una gráfica de su peso en la Luna, la Tierra, Mercurio Júpiter en un plano de coordenadas, con un color diferente para cada uno. La ecuación para Mercurio es = 0.8. La ecuación para Júpiter es =.5. Basándose en la gráfica, en qué planeta pesarían más? Menos? Cómo lo saben? Y su mascota? Cuánto pesaría en la Luna? Consideren usar las ecuaciones mencionadas para determinar el peso de otros objetos si estuviesen en otros planetas. Disfruten eplorando el espacio eterior juntos! 7 Algebra 1 Copright Big Ideas Learning, LLC

4 .1 Start Thinking Consider the equation =. Are there an values of that ou cannot substitute into the equation? If so, what are the? Are there an values of that ou cannot obtain as an answer? If so, what are the?.1 Warm Up In Eercises 1 9, use one coordinate plane to plot the points. 1. A (, ). B(, ). C(, 0). D(, ) 5. E( 7, ) 6. F( 6, 10) 7. G( 10, 7) 8. H ( 8, ) 9. I ( 9, ).1 Cumulative Review Warm Up Solve the inequalit. Graph the solution > 6. 7 m + 0. r 5 >. 10 w < 6 5. h j 10 + > p + p n 9 < 10 Copright Big Ideas Learning, LLC Algebra 1 7

5 Name Date.1 Practice A In Eercises 1 and, determine whether the relation is a function. Eplain. 1.. Input, 8 8 Output, 0 Input, Output, In Eercises and, determine whether the graph represents a function. Eplain In Eercises 5 and 6, find the domain and range of the function represented b the graph The function = 7 + 5represents the monthl cost (in dollars) of a group of members joining the fitness club. a. Identif the independent and dependent variables. b. Your group has enough mone for up to si members to join the fitness club. Find the domain and range of the function. In Eercises 8 and 9, determine whether the statement uses the word function in a wa that is mathematicall correct. Eplain our reasoning. 8. A function pairs each teacher with 0 students. 9. The cost of mailing the package is a function of the weight of the package. 7 Algebra 1 Copright Big Ideas Learning, LLC

6 Name Date.1 Practice B In Eercises 1 and, determine whether the relation is a function. Eplain. 1.. Input, Output, Input, 0 1 Output, In Eercises and, determine whether the graph represents a function. Eplain In Eercises 5 and 6, find the domain and range of the function represented b the graph The function = 18 represents the number of book raffle tickets and food raffle tickets ou bu at a club event. a. Solve the equation for. b. Make an input-output table to find ordered pairs for the function. c. Plot the ordered pairs in a coordinate plane. In Eercises 8 10, find the domain and range of the function. 8. = + 9. = = Copright Big Ideas Learning, LLC Algebra 1 75

7 Name Date.1 Enrichment and Etension A Quadratic Function: The Diving Problem You are jumping off the 10-foot diving board at the local pool. You bounce up at 6 feet per second and then drop toward the water. Your height h above the water, in terms of time t, follows the function shown. () ht = 16t + 6t + 10 a. Graph this function, with t on the horizontal ais. Fill in a table of values where the increments of time are tenths of a second. b. Eplain what the domain and range might be and wh. c. Eplain wh this situation is quadratic instead of linear. Give a graphical eplanation and a logical eplanation. d. Use the graph to determine the maimum height of our dive. e. Use the graph to determine when ou reach the maimum height of our dive. f. Use the graph to determine how long it takes ou to hit the water. g. Use the quadratic formula to prove our answer in part (f ). 76 Algebra 1 Copright Big Ideas Learning, LLC

8 Name Date.1 Puzzle Time What Has A Foot On Each End And One In The Middle? Write the letter of each answer in the bo containing the eercise number. Determine whether the relation is a function. 1. ( 8, 5 ), ( 6, ), (, 9 ), (, 6 ), (, 7). (, ), (, ), (, 7 ), ( 5, 1 ), ( 6, ) H. es I. no A. es B. no. ( 11,, ) ( 9,, ) ( 7,, ) ( 5,, ) (, ). ( 1, ), (, 1 ), (, ), (, ), (, ) A. es B. no B. es C. no 5. ( 17, ), (, ), ( 1, 1 ), (, ), ( 17, ) 6. (, 1, ) ( 1, 6, ) (,, ) ( 7, 8, ) ( 10, 1) C. es D. no K. es L. no Find the domain and range of the function represented b the graph S. D: 0 T. D: Q. D: 0 R. D: 0 < R: R: 0 R: 0 R: 0 < Use the following information to answer Eercises 9 and 10. The function t = 8j + represents the number of tomatoes t that our neighbor has left after making j jars of homemade salsa. 9. Identif the dependent variable. 10. Identif the independent variable. R. jars of salsa S. tomatoes Y. jars of salsa Z. tomatoes Copright Big Ideas Learning, LLC Algebra 1 77

9 . Start Thinking Plot the following points in a coordinate plane. ( 5,, ) (, 0, ) (,, ) (, ) Connect the points with a line. Name another point on the line. Is the point ( 1, ) on the line? How do ou know? If ( 1, ) is part of the relation, is it a function? Wh or wh not?. Warm Up Plot the coordinates from the table in a coordinate plane. Connect them with a line or smooth curve Cumulative Review Warm Up Solve the literal equation for. 1. = 5 7. a = 5z. = 5 r 5. s t = r 5. c = m = Algebra 1 Copright Big Ideas Learning, LLC

10 Name Date. Practice A In Eercises 1 and, determine whether the graph represents a linear or nonlinear function. Eplain. 1.. In Eercises and, determine whether the table represents a linear or nonlinear function. Eplain In Eercises 5 8, determine whether the equation represents a linear or nonlinear function. Eplain. 5. = = 7. = 9 8. = ( 1)( + 7) 9. Fill in the table so it represents a linear function In Eercises 10 and 11, find the domain of the function represented b the graph. Determine whether the domain is discrete or continuous. Eplain Copright Big Ideas Learning, LLC Algebra 1 79

11 Name Date. Practice B In Eercises 1 and, determine whether the graph represents a linear or nonlinear function. Eplain In Eercises and, determine whether the table represents a linear or nonlinear function. Eplain In Eercises 5 8, determine whether the equation represents a linear or nonlinear function. Eplain = = = = 0 7. ( )( ) In Eercises 9 and 10, determine whether the domain is discrete or continuous. Eplain. 9. Input Months, Output Height of basil plant (inches), Input Tickets, Output Cost (dollars), Algebra 1 Copright Big Ideas Learning, LLC

12 Name Date. Enrichment and Etension Linear Functions: Taking a Tai You take a trip to downtown Boston to walk the Freedom Trail with our famil. After ou walk through the Bunker Hill Memorial, our famil decides to take a tai to a restaurant for dinner. After 1 mile, the meter on the tai sas $.75. It will cost $8.5 to go miles. The cost varies linearl with the distance that ou traveled. a. Write the particular linear function that models the cost of our trip as a function of the distance traveled. Use the notation C( d ). b. Write the function using improper fractions. c. How much would it cost ou to travel 10 miles in a tai? d. How far can ou travel if ou onl have $10 to spend? e. Calculate the cost-intercept. What does this number represent? f. Plot the graph of this linear function. What is a suitable domain for this problem? What is a suitable range? g. What is the slope of the line? Show how to find it both graphicall and algebraicall. h. What does the slope of the line represent? i. Write our own linear function word problem, and prove that it works graphicall and algebraicall. Copright Big Ideas Learning, LLC Algebra 1 81

13 Name Date. Puzzle Time What Do You Get When You Cross A Tortoise And A Porcupine? Write the letter of each answer in the bo containing the eercise number. Determine whether the graph, table, or equation represents a linear or nonlinear function. 1.. D. linear E. nonlinear O. linear P. nonlinear A. linear B. nonlinear N. linear O. nonlinear 5. 1( ) = = W. linear X. nonlinear K. linear L. nonlinear 7. = = 8 11 P. linear Q. nonlinear K. linear L. nonlinear 9. The function = represents the cost (in dollars) of a large pizza with etra toppings. S. linear T. nonlinear Algebra 1 Copright Big Ideas Learning, LLC

14 . Start Thinking The range ( ) of a function is the result of performing one or more operations on all possible domain ( ) values. In the equation = + 1, the input ( ) is multiplied b and then added to 1. The value of depends on the value of. What is the function of the -values, 0, 1, and in the equation? Make up a new function and describe how to find the -values.. Warm Up Evaluate the epression for = 1, 0, and ( ) ( 5) 6. ( ) Cumulative Review Warm Up Solve the inequalit m < 8 + m. d + 1 > d 7 m. 9g + g + 5 g. 7 r ( b + 5) Copright Big Ideas Learning, LLC Algebra 1 8

15 Name Date. Practice A In Eercises 1, evaluate the function when =, 0, and f( ) =. g( ) =. h ( ) = 5. Let ct () be the number of customers in a department store t hours after 8 A.M. Eplain the meaning of each statement. a. c ( 0) = 10 b. c( 6) = c( 7) c. ck ( ) = 0 d. c( ) > c( ) In Eercises 5 8, find the value of so that the function has the given value. 5. f( ) = 6; f( ) = 6. g ( ) g ( ) = 10 ; = f( ) = 5; f( ) = 8. h ( ) h ( ) In Eercises 9 and 10, find the value of so that f( ) = 7. = 1 8 ; = 9. f f The function C ( ) = + represents the cost (in dollars) of cable for months, including the $5.50 installation fee. a. How much would ou have spent on cable after 6 months? b. How man months of cable service can ou have for $.50? In Eercises 1 15, graph the linear function. 1. r ( ) = 1. q ( ) = 1. g ( ) = 15. j ( ) 1 5 = Let f be a function. Use each statement to find the coordinates of a point on the graph of f. a. f ( ) is equal to 7. b. A solution of the equation f() t = is. 8 Algebra 1 Copright Big Ideas Learning, LLC

16 Name Date. Practice B In Eercises 1, evaluate the function when =, 0, and f( ) = g ( ) = h ( ) =. Let g( ) be the percent of our friends with a landline phone ears after 000. Eplain the meaning of each statement. a. g ( 0) = 100 b. g() 5 = g() 6 c. g( 10) = m d. g( 11) > g( 1) In Eercises 5 8, find the value of so that the function has the given value. 5. f( ) = 8 7; f( ) = g ( ) g ( ) = + 7; = 7 7. f( ) = 1 1; f( ) = 9 8. h ( ) h ( ) In Eercises 9 and 10, find the value of so that f( ) = 7. = 6 ; = f 8 f In Eercises 11 1, graph the linear function. 11. h ( ) = + 1. p ( ) 1 = 1 1. v ( ) = k ( ) = 15. The function C ( ) 5 75 = + represents the labor cost (in dollars) for Bob s Auto Repair to replace our alternator, where is the number of hours. The table shows sample labor costs from its main competitor, Budget Auto Repair. The alternator is estimated to take 5 hours of labor. Which compan would ou hire? Eplain. Hours 1 Cost $90 $10 $170 Copright Big Ideas Learning, LLC Algebra 1 85

17 Name Date. Enrichment and Etension Composition of Functions Function Composition, f ( g ( )) or ( f g)( ), is appling the results of one function to the results of another. To perform a composition, ou must combine the functions so that the output of one function becomes the input of another. Eample: If f( ) = and g ( ) = + 7, find f ( g ( )) and g f( ) ( ). ( ( )) ( ) ( ( )) ( ( )) = 10 f g f g f g = + 7 = 7 ( ( )) ( ) ( ( )) ( ( )) = + 1 g f g f g f = + 7 = In Eercises 1 6, perform the indicated operation if g ( ) = + 1, h ( ) = 5, and p ( ) =. 1. hg ( ( )). ( g g)( ). hg ( ( p ( ))). h ( ) + g ( ) 5. g( p( 5) ) 6. h ( ) g ( ) 7. You work 0 hours a week at a high-end clothing store. You make $180 ever week plus % commission on sales over $600. Assume ou sell enough this week f = and g ( ) = 600, to earn a commission. Given the functions ( ) 0.0 which composition of ( f g)( ) or ( g f)( ) represents our commission? 8. You make a purchase at a local furniture store, but the furniture ou bu is too big to bring home ourself, so ou have to have it delivered for a small fee. You pa for our purchase plus the sales ta and the fee. The sales ta is 7% while the fee is $0. a. Write a function p( ) for the total purchase, including onl the deliver fee. b. Write a function t ( ) for the total purchase, including onl ta and not the deliver fee. c. Calculate ( p t)( ) and ( t p)( ). a lower cost? Then interpret both. Which results in d. If the furniture store is not allowed to ta the deliver fee, which is the appropriate composition for our situation? 86 Algebra 1 Copright Big Ideas Learning, LLC

18 Name Date. Puzzle Time How Does A Bee Get To School? Circle the letter of each correct answer in the boes below. The circled letters will spell out the answer to the riddle. Evaluate the function for the given value of. 1. g ( ) = 7; =. f( ) = ; = 6 k 11; 1. ( ) = =. ( ) 1 t = 9+ 10; = 6 5. g ( ) 7 15 ; 8 = = 6. c ( ) = 0.5 ; = 10 w 1 6 1; 7. ( ) 1 1 p = + 6 1; = 8 = = 8. ( ) ( ) Find the value of so that the function has the given value. 5 = ; = b ( ) = 8; b ( ) = h ( ) h ( ) = 8 17; = n ( ) = ; n ( ) = 8 1. r ( ) r ( ) = + 19; = 0 1. s ( ) s ( ) 1. The local cable compan charges $90 per month for basic cable and $1 per month for each additional premium cable channel. The function c ( ) = represents the monthl charge (in dollars), where represents the number of additional premium channels. How man additional premium channels would ou have ordered if our bill was $11 per month? B I V T K T C A J E K I G E O S M T N H S E D B R U F A Z Q P Z Copright Big Ideas Learning, LLC Algebra 1 87

19 . Start Thinking Equations are useful because the give ou a wa to represent what happens to when the value of is changed. Think of a situation ou can represent with and. Write an equation to show their relationship. For our situation, what does it mean when = 0? When = 0? Eplain how thinking of these two instances can help ou graph our equation.. Warm Up Write a rule to relate the variables in the table Cumulative Review Warm Up Solve the equation. Justif each step. Check our solution. 1. 6g = 18. p 6 =. 7r = 6. = Algebra 1 Copright Big Ideas Learning, LLC

20 Name Date. Practice A In Eercises 1, graph the linear equation. 1. =. =. = In Eercises 7, find the - and -intercepts of the graph of the linear equation.. 5 = = = = In Eercises 8 1, use intercepts to graph the linear equation. Label the points corresponding to the intercepts = = = = = = 1. A dance team has two competitions on the same da. The coaches decide to split the 96-member team, sending some to each competition. Competition A requires four-member dance teams per event, and Competition B requires si-member dance teams per event. The equation + 6 = 96 models this situation, where is the number of four-member teams and is the number of si-member teams. a. Graph the equation. Interpret the intercepts. b. Find four possible solutions in the contet of the problem. 15. Describe and correct the error in finding the intercepts of the graph of the equation. The intercept is at 16. Write an equation in standard form of a line whose intercepts are fractions. Eplain how ou know the intercepts are fractions. Copright Big Ideas Learning, LLC Algebra 1 89

21 Name Date. Practice B In Eercises 1, graph the linear equation. 1. = 1. =. = 0 In Eercises 7, find the - and -intercepts of the graph of the linear equation = = 5 6. = = In Eercises 8 1, use intercepts to graph the linear equation. Label the points corresponding to the intercepts = = = = = 1. + = Your club is ordering enrollment gifts engraved with our club logo. Ke chains cost $5 each. Wristbands cost $ each. You have a budget of $150 for the gifts. The equation 5 + = 150 models the total cost, where is the number of ke chains and is the number of wristbands. a. Graph the equation. Interpret the intercepts. b. Your club decides to order 18 ke chains. How man wristbands can ou order? 15. Describe and correct the error in finding the intercepts of the graph of the equation. The -intercept is at and the -intercept is at 16. Write an equation in standard form of a line whose -intercept is an integer and -intercept is a fraction. Eplain how ou know that the -intercept is an integer and the -intercept is a fraction. 90 Algebra 1 Copright Big Ideas Learning, LLC

22 Name Date. Enrichment and Etension Challenge: - and -intercepts In Eercises 1 1, find the - and -intercepts for the given equation. Assume that a, b, and c are all nonzero real numbers. 1. a + b = c. a + b = c. a + b = c. c + a + b = c 5. a + b c = 6. + b + c = 5c 7. b + = 6c 8. a = c 5 + = = 7 a+ b= 6ab = Copright Big Ideas Learning, LLC Algebra 1 91

23 Name Date. Puzzle Time Wh Did The Horse Go To The Doctor? Write the letter of each answer in the bo containing the eercise number. Find the - and -intercepts of the graph of the linear equation =. 6 = = = = 6. 7 = = 1 1 = = = The student council is responsible for setting up the tables for an awards banquet at the end of the ear. The council members need to decide what tables the should use. Eight people can sit at a circular table, while 1 people can sit at a rectangular table. There are 1 people who confirmed that the would attend. The equation = 1 models this situation, where is the number of circular tables and is the number of rectangular tables. Find the - and -intercepts. Answers E. -intercept: (, 0) ; -intercept: ( 0, ) R. -intercept: (, 0) ; -intercept: ( 0, ) Y. -intercept: (, 0 ); -intercept: ( 0, 1) O. -intercept: ( 6, 0 ); -intercept: ( 0, ) F. -intercept: ( 1, 0) ; -intercept: none A. -intercept: ( 5, 0 ); -intercept: ( 0, ) V. -intercept: (, 0) ; 1 -intercept: 0, 7 R. -intercept: none; -intercept: ( 0, ) H. -intercept: ( 18, 0 ); -intercept: ( 0, 1 ) F. -intercept: ( 5, 0 ); -intercept: ( 0, 7) E. -intercept: ( 8, 0 ); -intercept: ( 0, 6 ) 9 Algebra 1 Copright Big Ideas Learning, LLC

24 .5 Start Thinking Tractor-trailers often weigh in ecess of 50,000 pounds. With all the weight on board, these trucks need an etra warning when traveling down steep hills. Research the term roadwa grade and eplain its importance to tractor-trailer drivers. How would ou represent a 1% grade as a fraction when traveling downhill?.5 Warm Up Make a table of points and plot them in a coordinate plane. Connect the points with a line. 1. =. = =. = = 5 6. = 0.5 Cumulative Review Warm Up Solve the inequalit. Graph the solution, if possible. 1. >. d 8 <. s p > h c 7 < n > 1 Copright Big Ideas Learning, LLC Algebra 1 9

25 Name Date.5 Practice A In Eercises 1 and, describe the slope of the line. Then find the slope. 1.. (, ) (, ) (1, 1) 1 (, 1) In Eercises and, the points represented b the table lie on a line. Find the slope of the line In Eercises 5 8, find the slope and the -intercept of the graph of the linear equation. 5. = = 7 7. = 8. = 9 In Eercises 9 1, graph the linear equation. Identif the -intercept. 9. = = = 1. + = In Eercises 1 and 1, graph the function with the given description. Identif the slope, -intercept, and -intercept of the graph. 1. A linear function f models a relationship in which the dependent variable decreases units for ever units the independent variable increases. The value of the function at 0 is A linear function g models a relationship in which the dependent variable increases units for ever 7 units the independent variable increases. The value of the function at 0 is 1. 9 Algebra 1 Copright Big Ideas Learning, LLC

26 Name Date.5 Practice B In Eercises 1 and, describe the slope of the line. Then find the slope. 1.. (, 1) (0, ) (, 1) (, ) In Eercises and, the points represented b the table lie on a line. Find the slope of the line In Eercises 5 8, find the slope and the -intercept of the graph of the linear equation. 5. = = 7 7. = = + 1 In Eercises 9 1, graph the linear equation. Identif the -intercept. 9. = = = = 0 1. A linear function g models the growth of our hair. On average, the length of a hair strand increases 1.5 centimeters ever month. a. Graph g when g ( 0) = 10. b. Identif the slope and interpret the -intercept of the graph. c. B how much, in inches, does the length of a hair strand increase each month? In Eercises 1 and 15, find the value of k so that the graph of the equation has the given slope or -intercept. 1. = 6k ; m = = + k; b = 8 Copright Big Ideas Learning, LLC Algebra 1 95

27 Name Date.5 Enrichment and Etension Challenge: Slope and Slope-Intercept Form In Eercises 1, find the slope of the line through the given points. Assume that a and b are nonzero real numbers. 1. ( a, b) and (, 1). ( a, b) and ( a, b). ( a, b) and ( b, a ). ( 5 a, b) and ( 5 b, a) Two lines are parallel if the both have the same slope. Two lines are perpendicular if the product of their slopes is 1, unless the slopes are 0 and undefined. In Eercises 5 8, find the value of so that the line through the pair of points is parallel to a line with the slope given. Then find the value of so that the line through the pair of points is perpendicular to a line with the slope given. 5. m = 1; (, ) and ( 1, ) 6. m = 0; (, ) and ( 5, ) 7. m = ; (, ) and (, 5) 8. m = 5; ( 1, ) and (, ) 96 Algebra 1 Copright Big Ideas Learning, LLC

28 Name Date.5 Puzzle Time What Did The Pelican Sa When It Finished Shopping? Write the letter of each answer in the bo containing the eercise number. Find the slope of the line passing through the given points. 1. ( 10, 1, ) ( 8, 8, ) ( 6,, ) (, 0). (, ), ( 0, 1 ), (, 0 ), ( 8, 1). ( 7, 7 ), ( 0, 8 ), ( 7, 9 ), ( 1, 10). (, ), ( 0, ), (, ), (, 5) 5. (, 11 ), (, 5 ), ( 6, 9 ), ( 8, 5) 6. ( 11, 8 ), ( 5, 1 ), ( 1, 10 ), ( 7, ) Find the slope and the -intercept of the graph of the linear equation. 7. = = 9. + = = = = 0 1. The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. The function C ( ) = represents the cost C (in dollars) of towing a vehicle, where is the number of miles the vehicle is towed. Identif the slope and -intercept. Answers I. m = 1 M. m = 6, b = U. 1 m = N. m =, b = 1 P. m =, b = 6 I. m = 7 L. 1 m =, b = O. m = L. m = T. 1 m = 0, b = B. m = 8, b = 50 Y. T. 1 m = m =, b = Copright Big Ideas Learning, LLC Algebra 1 97

29 .6 Start Thinking Graph the lines = and = 5. Note the change in slope of the line. Graph the line = 0. What is happening to the line? What would the line look like if the slope was changed to 100? 1000? What if the slope was the greatest number ou can think of? Eplain how this shows the slope of a vertical line is undefined..6 Warm Up Graph the point and its image in a coordinate plane. 1. P( 5, ); reflected in the -ais. Q(, ); reflected in the -ais. R( 1, 5 ); reflected in the line through (, ) and (, ). S ( 5, 1 ); reflected in the line through (, ) and ( 8, ).6 Cumulative Review Warm Up Solve the equation. 1. c c =. ( q ). ( g ) = q 5 10 = 6 1g. m + = w 9w 1 = 6. k ( k ) + + = 9 98 Algebra 1 Copright Big Ideas Learning, LLC

30 Name Date.6 Practice A In Eercises 1 and, use the graphs of f and g to describe the transformation from the graph of f to the graph of g. 1. f() = +. g() = f() 5 g() = f( + 1) f() =. You and a friend start running from the same location. Your distance d (in miles) after t minutes is dt () = 1 7 t. Your friend starts running 10 minutes after ou. Your friend s distance f is given b the function f() t = d( t 10 ). Describe the transformation from the graph of d to the graph of f. In Eercises and 5, use the graphs of f and h to describe the transformation from the graph of f to the graph of h f() = + 5 h() = f( ) f() = h() = f() 8 In Eercises 6 and 7, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. 6. f ( ) = + ; r( ) = f( ) 7. f ( ) = + 6; r( ) = 1 f( ) In Eercises 8 and 9, write a function g in terms of f so that the statement is true. 8. The graph of g is a vertical translation units down of the graph of f. 9. The graph of g is a reflection in the -ais of the graph of f. Copright Big Ideas Learning, LLC Algebra 1 99

31 Name Date.6 Practice B In Eercises 1 and, use the graphs of f and g to describe the transformation from the graph of f to the graph of g. 1. f( ) = ; g( ) = f( + 5). f( ) = 1 ; g( ) = f( 6). The total cost C (in dollars) to rent a 1-foot b 0-foot canop for d das is given b the function Cd ( ) = 15d + 0, where the setup fee is $0 and the charge per da is $15. The setup fee increases b $0. The new total cost T is given b the function Td ( ) = Cd ( ) + 0. Describe the transformation from the graph of C to the graph of T. In Eercises and 5, use the graphs of f and h to describe the transformation from the graph of f to the graph of h.. f ( ) = ; h( ) = f( ) 5. f ( ) = 1 + 1; h( ) = f( ) In Eercises 6 and 7, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. 6. f ( ) 5 10; r( ) f ( ) = = 7. f ( ) = 1 + ; r( ) = 6 f( ) 5 In Eercises 8 11, use the graphs of f and g to describe the transformation from the graph of f to the graph of g. = + = 9. f ( ) = + 6; g( ) = f ( ) 8. f( ) 5; g( ) f( ) 10. f ( ) = ; g( ) = 1 f( ) 11. f( ) g( ) f( ) = ; = + In Eercises 1 and 1, write a function g in terms of f so that the statement is true. 1. The graph of g is a horizontal shrink b a factor of of the graph of f. 1. The graph of g is a horizontal translation 5 units left of the graph of f. In Eercises 1 17, graph f and h. Describe the transformations from the graph of f to the graph of h. 1. f( ) = ; h( ) = ( ) ( ) f = ; h = f( ) = ; h( ) = ( ) ( ) f = ; h = Algebra 1 Copright Big Ideas Learning, LLC

32 Name Date.6 Enrichment and Etension Multiple Transformations of Linear Equations Eample: Let f( ) = 1. Graph the transformation g ( ) f( ) Use composition of functions to rewrite g( ). Then find g( 1, ) g( 0, ) and g( 1) check our graph. f() = 1 ( ) ( ( ) ) ( ) = ( ) + ( ) = g g g = = 1 +. to g ( ) ( ) () 1 = 8 g 0 = g 1 = 0 g() = f( 1) + Let f( ). rewrite ( ). = + Graph each transformation given. Use composition of functions to g Then find g( ) g( ) g( ), 0, and 1. 1 g = f 1. ( ) 1 5. g ( ) = f( + ) +. g ( ) f( ) = What is different about Eercise? Is it possible to write a rule for this tpe of transformation? If so, please demonstrate. Copright Big Ideas Learning, LLC Algebra 1 101

33 Name Date.6 Puzzle Time What Did One Watch Sa To The Other Watch? Write the letter of each answer in the bo containing the eercise number. Describe the transformations from the graph of f to the graph of g. 1. f( ) = 7; g( ) = f( ) 5. f ( ) = + 9; g( ) = f( ) 1 f = g = f. ( ) 6 11; ( ) = 18; =. f( ) g( ) f( ) 5. f ( ) = ; g( ) = 8 f ( ) f = ; g = ( ) ( ) 9 f = g = ( ) ; ( ) 1 f = ; g = 6 8. ( ) ( ) f = ; g = 9. ( ) ( ) 10. Members of the marching band need to rent a moving van to haul their instruments back and forth to several competitions. The total cost C (in dollars) to rent a moving van for m miles is given b the function Cm ( ) = m + 5, where the flat fee is $5 and the charge per mile is $. The flat fee decreases b $5. The new total cost T is given b the function Tm ( ) = Cm ( ) 5. Describe the transformation from the graph of C to the graph of T. Answers G. vertical stretch b a factor of 8 I. reflection in the -ais and a vertical translation 9 units up 16 A. reflection in the -ais T. horizontal stretch b a factor of and a vertical translation 6 units down N. vertical translation 5 units down U. vertical translation units down E. horizontal translation units right M. horizontal shrink b a factor of 1 and a vertical translation units down T. vertical translation 6 units up O. horizontal stretch b a factor of Algebra 1 Copright Big Ideas Learning, LLC

34 .7 Start Thinking Use a graphing calculator to graph the function f ( ) =. Sketch the graph on a coordinate plane. Describe the graph of the function. Now graph the functions g ( ) 5, and h ( ) 5 the same coordinate plane. Eplain wh the graphs of g ( ) and h ( ) are not the same. = + = + on.7 Warm Up Solve the equation, if possible. 1. n 8 =. b 5 = 1. z + = 10. t + 5 = n = h 1 = 7 7. n + = t + 7 =.7 Cumulative Review Warm Up Write the sentence as an inequalit. Then solve the inequalit. 1. A number minus 7 is less than 1.. A number plus is at most.. The sum of a number and 8 is greater than 5.. The number 5 is greater than or equal to the difference of a number and 16. Copright Big Ideas Learning, LLC Algebra 1 10

35 Name Date.7 Practice A In Eercises 1, graph the function. Compare the graph to the graph of f = Describe the domain and range. ( ). 1. g ( ) =. p ( ) = + 1. h ( ) = + 5. k ( ) = 1 In Eercises 5 and 6, graph the function. Compare the graph to the graph of f = + ( ). 5. h ( ) = + 6. h ( ) = + In Eercises 7 and 8, compare the graphs. Find the value of h, k, or a g() = + k f() = f() = h() = h In Eercises 9 and 10, write an equation for h() that represents the given g = transformation(s) of the graph of ( ). 9. vertical translation units up 10. vertical stretch b a factor of In Eercises 11 and 1, graph and compare the two functions. f = ; g = 11. ( ) ( ) m = + 5; n = ( ) ( ) 1 1. The number of ice cream cones sold c (in hundreds) increases and then decreases as described b the function ct () = 5 t 6 + 0, where t is the time (in months). a. Graph the function. b. What is the greatest number of ice cream cones sold in 1 month? 10 Algebra 1 Copright Big Ideas Learning, LLC

36 Name Date.7 Practice B In Eercises 1, graph the function. Compare the graph to the graph of f = Describe the domain and range. ( ). 1. m ( ) =. t ( ) =. g( ) =. z ( ) = In Eercises 5 and 6, graph the function. Compare the graph to the graph of f = + ( ). 5. k ( ) = q ( ) = In Eercises 7 and 8, compare the graphs. Find the value of h, k, or a f() = f() = s() = a w() = a In Eercises 9 and 10, write an equation for h() that represents the given g = transformation(s) of the graph of ( ). 9. horizontal translation 7 units right 10. vertical shrink b a factor of 1 and a reflection in the -ais In Eercises 11 and 1, graph and compare the two functions. c = + ; d = ( ) ( ) p = + 1 ; q = ( ) ( ) 1. Graph = + 5 and = 8 in the same coordinate plane. Use the graph to solve the equation + 5 = 8. Check our solutions. Copright Big Ideas Learning, LLC Algebra 1 105

37 Name Date.7 Enrichment and Etension Transformations and Compositions Eample: Graph = 1 +, and then state the domain and range in interval notation. First graph the function on the inside of the outer absolute value. Then invert all the negative -values to positive -values, because the final output of this particular absolute value function must be all positive numbers. domain: (, ) range: [ 0, ) In Eercises 1 6, graph each function and state the domain and range in interval notation. 1. =. = 1. = = 5. = 6. = Algebra 1 Copright Big Ideas Learning, LLC

38 Name Date.7 Puzzle Time What Do Sharks Eat For Dinner? Write the letter of each answer in the bo containing the eercise number. Describe the transformations from the graph of f to the graph of g. f = ; g = ( ) ( ) f = ; g =. ( ) ( ). ( ) ; ( ) f = g = 1 f = g =. ( ) ; ( ) f = 7; g = 7 5. ( ) ( ) f = + 1; g = ( ) ( ) f = + 9 6; g = ( ) ( ) f = ; g = ( ) ( ) Write an equation that represents the given f = transformation(s) of the graph of ( ). 9. horizontal translation units left and a reflection in the -ais 10. vertical stretch b a factor of and a reflection in the -ais 11. a reflection in the -ais and a vertical translation units up 1. horizontal shrink b a factor of 1 and a vertical Answers I. g ( ) = + P. reflection in the -ais F. horizontal translation units right and vertical translation 8 units up N. reflection in the -ais and a vertical stretch b a factor of D. vertical shrink b a factor of 1 H. horizontal translation units right and vertical translation units down A. vertical translation 6 units up H. g ( ) = + C. g( ) = I. g ( ) = S. horizontal translation units right S. horizontal shrink b a factor of 1 translation units down Copright Big Ideas Learning, LLC Algebra 1 107

39 Name Date Chapter Cumulative Review Solve the equation and check our answer = 0. 9b = 7. = h + = 5. j 9π 1π 1 1 w 0.5 = = 6. ( ) = = 17u u 9. z 1 = 0 Write and solve an equation to answer the question. 10. It costs $51 for ou and our two friends to go skiing for the weekend. How much does it cost for just ou to go skiing for the weekend? 11. Your four-month bill for the gm comes to $1. That includes the cost per month of $50 plus the one-time membership fee. How much is the membership fee? Solve the equation. Check our solution. 1. ( r ) = ( + 5) = ( + ) 1. + ( ) = + 8( 5) ( 8z + 0) = 1 ( 18z + 16) Your cell phone compan offers ou a choice between two promotional deals. You can either get 500 free tet messages with a charge of $0.10 for each tet message over 500, or ou can get 00 free tet messages with a charge of $0.0 for each tet message over 00. How man tet messages would ou have to send for the cost to be the same for either plan? Solve the equation. Determine whether the equation has one solution, no solution, or infinitel man solutions. = v 60 = ( 0 5v) 19. ( ) ( 1) Solve the equation. Graph the solutions, if possible. = = 1. d = 6. r 6 = 1. = Torque is a measure of how much to tighten a bolt. The torque specification for a small-block Chev V8 is 70 foot-pounds with an error of 0.0 foot-pounds. Write and solve an absolute value equation to find the minimum and maimum torque required for the bolts. 108 Algebra 1 Copright Big Ideas Learning, LLC

40 Name Date Chapter Cumulative Review (continued) Write the sentence as an inequalit. 5. A number n is at least The number 50 is no more than a number h times. Solve the inequalit. Graph the solution. b + 8. ( t) Write the sentence as an inequalit. Then solve the inequalit. 0. The difference of 5 and a number is at least A number plus 1 is no more than. Solve the inequalit. Graph the solution, if possible.. 8w 7 w 56 > z + 8z < 10 + <. ( g ) > g. 7( h 1) 7( 8 h) 5. < 9 + n < 6. 5w > 5 and 7w 7. t or + t 0 Solve the inequalit. Graph the solution, if possible < w < 5 Determine whether the relation is a function. Eplain. 1. (, ), (, 5 ), (, 7 ), (, 8 ), ( 9, 10). ( 5, ), (, 8 ), ( 0, 1 ), (, 7 ), ( 5, 11). (,, ) ( 7,, ) ( 9,, ) (,, ) (, ). ( 1, ), ( 7, 11 ), ( 0, ), ( 1, 8 ), ( 1, 67) Input 0 Output Find the domain and range of each relation, and determine whether or not the graph represents a function Copright Big Ideas Learning, LLC Algebra 1 109

41 Name Date Chapter Cumulative Review (continued) 50. The function = + represents the amount of mone left in our school lunch account (in dollars) after das. a. Identif the independent and dependent variables. b. There are 10 das left in the school ear. Find the domain and range of the functions. Determine whether the table represents a linear or nonlinear function. Eplain Input 6 8 Output Determine whether the equation represents a linear or nonlinear function. Eplain. 5. = 5. 5 Evaluate the function when =, 0, and. + = 55. = ( ) 56. f( ) = g ( ) = h ( ) = 1 Find the value of so that the function has the given value. 59. f( ) = ; f( ) = 60. r ( ) = 1 + ; r ( ) = 61. q ( ) q ( ) Graph the linear function. 6. f ( ) = 6. w ( ) = 1 6. h ( ) = =, 0 represents the average speed of a car that took a 108-mile trip in hours. 65. The function f ( ) a. What was the average speed of the car if the trip took hours? b. How long did the trip take if the average speed was 5 miles per hour? Find the - and -intercepts of the graph of the linear equation = = = 1 = + 1; = Algebra 1 Copright Big Ideas Learning, LLC

42 Name Date Chapter Cumulative Review (continued) Use intercepts to graph the linear equation. Label the points corresponding to the intercepts = = = 7 7. You are ordering warm-up clothes for the basketball team. The mesh shirts cost $16 each and the cotton shirts cost $8 each. You have a budget of $0 for the shirts. The equation = 0 models the total cost, where is the number of mesh shirts and is the number of cotton shirts. a. Graph the equation. Interpret the intercepts. b. Four plaers decide the want the cotton shirts. How man mesh shirts can ou order? The following points lie on a line. Find the slope of the line. 7. ( 1,, ) (, 6, ) (, 9, ) (, 1, ) ( 5, 15 ) 7. (, ), ( 0, ), (, 6 ), (, 10 ), ( 6, 1) Find the slope and -intercept. Then graph the linear equation. 75. = = 77. = 8 Use the graphs of f and g to describe the transformation from the graph of f to the graph of g. 78. f( ) = 1; g ( ) = f( ) = + ; g ( ) = Write a function g in terms of f so that the statement is true. 80. The graph of g is a vertical stretch b a factor of of the graph of f. 81. The graph of g is a horizontal translation units right of the graph of f. Graph the function. Compare the graph to the graph of f( ) domain and range. =. Describe the 8. t ( ) = r ( ) = 8. h ( ) = 1 Graph and compare the two functions. 85. f( ) = + ; g ( ) = h ( ) = 1 ; t ( ) = 1 Copright Big Ideas Learning, LLC Algebra 1 111