4.5 Practice B. 4.5 Practice A. Name Date. Possible zeros: Possible zeros: 5. Justify. your answer. your answer. In Exercises 1 6, solve the equation.

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1 Practice A Practice B In Eercises, solve the equation.. q q 0q 0. k + k + 9k 0.. p p. 8u u n + n 9n 8 0 In Eercises 7 0, find the zeros of the function. Then sketch a graph of the function. 7. f + 8. g h 0. f. According to the Rational Root Theorem, which is not a possible solution of the equation + + 0? In Eercises, solve the equation h h w + 8 8w. q 8q + 0. p p 0 p In Eercises 7 0, find the zeros of the function. Then sketch a graph of the function. 7. f g 9. h + 0. f 9 +. According to the Rational Root Theorem, which is not a possible zero of the f + 7? function A. B. C. D. A. B. C. D Describe and correct the error in listing the possible rational zeros of the function.. Describe and correct the error in listing the possible rational zeros of the function. Possible zeros: Possible zeros: In Eercises and, find all the real solutions of the equation Write a third or fourth degree polnomial function that has zeros at ±. Justif our answer. In Eercises and, find all the real solutions of the equation Write a third or fourth degree polnomial function that has zeros at ± 7. Justif our answer.. Determine the value of k for each equation so that the given -value is a solution k 0; a. + k 0; b.. The sidewalk hazard marker is shaped like a pramid, with a height centimeters greater than the length of each side of its square base. The volume of the marker is 97 cubic centimeters. What are the dimensions of the sidewalk hazard marker? +! WARNING Algebra Copright Big Ideas Learning, LLC 7

2 Practice A Practice B In Eercises, identif the number of solutions or zeros In Eercises, identif the number of solutions or zeros q q + 7q 0 r + r 7r 0. 8q q + 7q 0 9r + r 7r 0 In Eercises 8, find all zeros of the polnomial function. f. f g h In Eercises 9 and 0, determine the number of imaginar zeros for the function with the given degree and graph. Eplain our reasoning. 9. Degree: 0. Degree: In Eercises 8, find all zeros of the polnomial function. h + +. f g f In Eercises 9 and 0, determine the number of imaginar zeros for the function with the given degree and graph. Eplain our reasoning. 9. Degree: 0. Degree: In Eercises, write a polnomial function f of least degree that has rational coefficients, a leading coefficient of, and the given zeros..,,.,,., Write a polnomial function of degree with zeros,, and i. Justif our answer. In Eercises 7, determine the possible numbers of positive real zeros, negative real zeros, and imaginar zeros for the function. g +.. g + 0 g + 7. In Eercises, write a polnomial function f of least degree that has rational coefficients, a leading coefficient of, and the given zeros.., + i., i i., 7 Two zeros of f are i and. i Eplain wh the third zero must be a real number.. Use Descartes Rule of Signs to determine which function has no positive real zeros. A. f + 7 B. f + + C. f D. f Algebra Copright Big Ideas Learning, LLC

3 8 Practice A 8 Practice B In Eercises, graph the function.. f ( + ) ( ). g ( ) ( + )( + ). h ( )( )( + ) f ( ) ( + ). Describe and correct the error in using factors to graph f ( ) ( + ). In Eercises, graph the function.. f ( + ) ( ). g ( )( + )( ). h ( )( )( + 8) f ( )( + + ) f +.. Describe and correct the error in using factors to graph In Eercises 9, find all real zeros of the function.. f + 7. f f + 9. f In Eercises 0, graph the function. Identif the -intercepts and the points where the local maimums and local minimums occur. Determine the intervals for which the function is increasing and decreasing. 0. f +. + g. h +. f + In Eercises and, estimate the coordinates of each turning point. State whether each is a local maimum or a local minimum. Then estimate the real zeros and find the least possible degree of the function.. In Eercises 9, find all real zeros of the function.. f f f f In Eercises 0, graph the function. Identif the -intercepts and the points where the local maimums and local minimums occur. Determine the intervals for which the function is increasing and decreasing. 0. f g 0.. h 9. f + + You are making a rectangular bo out of a -inch b 8-inch piece of cardboard. The bo will be formed b making the cuts shown in the diagram and folding up the sides. You want the bo to have the greatest volume possible. a. How long should ou make the cuts? b. What is the maimum volume? c. What are the dimensions of the finished bo? in. 8 in. Algebra Copright Big Ideas Learning, LLC

4 . Practice A. Practice B In Eercises, find the indicated real nth root(s) of a.. n, a. n, a 9. n, a 8 In Eercises 9, evaluate the epression without using a calculator In Eercises 0, evaluate the epression using a calculator. Round our answer to two decimal places when appropriate. 0.,807.,.. 9. In Eercises and 7, find the radius of the figure with the given volume.. V 7 in. 7. V 7 m In Eercises, find the indicated real nth root(s) of a.. n, a. n, a. n, a In Eercises 9, evaluate the epression without using a calculator ( ) In Eercises 0, evaluate the epression using a calculator. Round our answer to two decimal places when appropriate ,. 70 ( ). 7 In Eercises and 7, find the radius of the figure with the given volume.. V in. 7. V 8 m h in. r h 7 in. r r r In Eercises 8, find the real solution(s) of the equation. Round our answer to two decimal places when appropriate ( 7) When the average price of an item increases from p to p over a period of p is given b n ears, the price p p r +, where r is the annual rate of inflation (in decimal form). Find the annual rate of inflation when the price of a loaf of bread was $.9 in 970 and $.9 in 00. n In Eercises 8, find the real solution(s) of the equation. Round our answer to two decimal places when appropriate Kepler s third law states that the relationship between the mean distance d (in astronomical units) of a planet from the Sun and the time t (in ears) it takes the planet to orbit the Sun can be given b d t. a. It takes Venus 0. ear to orbit the Sun. Find the mean distance of Venus from the Sun (in astronomical units). b. The mean distance of Jupiter from the Sun is. astronomical units. How man ears does it take Jupiter to orbit the Sun? 8 Algebra Copright Big Ideas Learning, LLC 9

5 . Practice A. Practice B In Eercises, use the properties of rational eponents to simplif the epression.. ( 7 ).. In Eercises, use the properties of rational eponents to simplif the epression In Eercises 7, use the properties of radicals to simplif the epression In Eercises 8, write the epression in simplest form In Eercises 9, simplif the epression ( ) + 79 ( ) The volume of a cube is 80 cubic centimeters. 0 + a. Use eponents to solve the formula for the volume V of a cube with side length s, V s, for s. b. Substitute the epression for s from part (a) into the formula for the surface area of a cube, S s. c. Substitute the volume of the given cube into the formula found in part (b) to find the surface area, S. Simplif, if possible. In Eercises 7, use the properties of radicals to simplif the epression In Eercises 8, write the epression in simplest form In Eercises 9, simplif the epression. 9. 0( ) ( ) ( 7 ) + ( 89 ). The volume of a right circular clinder is V 9 πr, where r is the radius. a. Use radicals to solve V 9π r for r. Simplif, if possible. b. Substitute the epression for r from part (a) into the formula for the surface area of a right clinder, S 8 πr + πr. c. Use the answer to part (b) to find the surface area of a right clinder when the volume is 08 cubic meters. Algebra Copright Big Ideas Learning, LLC

6 . Practice A. Practice B In Eercises, graph the function. Identif the domain and range of the function.. g +. h. f h. f. g + In Eercises 7, describe the transformation of f represented b g. Then graph each function. 7. f ; g + 8. f ; g + 9. f ; g 0. f g. f ; g ( ). ; ; + f g In Eercises, use a graphing calculator to graph the function. Then identif the domain and range of the function.. f. g h + In Eercises and 7, write a rule for g described b the transformations of the graph of f.. Let g be a vertical shrink b a factor of, followed b a translation units right of the graph of f Let g be a reflection in the -ais, followed b a translation units down of the graph of f +. In Eercises 8 and 9, use a graphing calculator to graph the equation of the parabola. Identif the verte and the direction that the parabola opens In Eercises 0 and, use a graphing calculator to graph the equation of the circle. Identif the radius and the intercepts In Eercises, graph the function. Identif the domain and range of the function.. g +. f. f + h. g ( ). h In Eercises 7, describe the transformation of f represented b g. Then graph each function. 7. f ; g 8. f g 9. f ; g ( ) 0. ; f ; g. f ; g +. f g ; In Eercises, use a graphing calculator to graph the function. Then identif the domain and range of the function.. g f +. h + In Eercises and 7, write a rule for g described b the transformations of the graph of f.. Let g be a horizontal stretch b a factor of, followed b a translation units up of the graph of f. 7. Let g be a translation unit up and units left, followed b a reflection in the -ais of the graph of f ( ). In Eercises 8 and 9, use a graphing calculator to graph the equation of the parabola. Identif the verte and the direction that the parabola opens In Eercises 0 and, use a graphing calculator to graph the equation of the circle. Identif the radius and the intercepts Algebra Copright Big Ideas Learning, LLC 9

7 . Practice A. Practice B In Eercises, solve the equation. Check our solution Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled b h. t + 7.8, where t is the age (in ears) of the elephant. Determine the age of an elephant with a shoulder height of 00 centimeters. In Eercises 8, solve the equation. Check our solution(s) In Eercises, solve the equation. Check our solution(s) Describe and correct the error in solving the equation In Eercises 8 0, solve the inequalit. +. ( ) > 0. The length (in inches) of a standard nail can be modeled b d, where d is the diameter (in inches) of the nail. a. What is the diameter of a standard nail that is inches long? b. What is the diameter of a standard nail that is inches long? c. The nail in part (b) is twice as long as the nail in part (a). Is the diameter twice as long? Eplain. In Eercises, solve the equation. Check our solution In Eercises 7, solve the equation. Check our solution(s) In Eercises, solve the equation. Check our solution(s). ( 8) + 0. ( 8). 0 8 In Eercises 8, solve the inequalit < 9. Hang time is the time ou are suspended in the air during a jump. Your hang time t in seconds is given b the function t 0. h, where h is the height (in feet) of the jump. A kite sailor has a hang time of. seconds. Find the height of the kite sailor's jump. In Eercises 0, solve the nonlinear sstem. Justif our answer with a graph The speed s (in miles per hour) of a car can be given b s 0 fd, where f is the coefficient of friction and d is the stopping distance (in feet). The coefficient of friction for a snow road is 0.0. You are driving 0 miles per hour and approaching an intersection. How far awa from the intersection must ou begin to brake? Algebra Copright Big Ideas Learning, LLC

8 . Practice A In Eercises and, find ( f + g) and ( f g) and state the domain of each. Then evaluate f f g. + g and f g for the given value of. ; ; 8 f + g + 9 ; 7;. f In Eercises, find ( fg) and g and state the domain of each. Then evaluate fg and f for the given value of. g f ; g ; 9. f g 0 ; ; 8 f g. ; ; 7. Practice B In Eercises and, find ( f + g) and ( f g) and state the domain of each. Then evaluate f f g. + g and f g for the given value of. ; 9 ; f g ; ;. f In Eercises, find ( fg) and g and state the domain of each. Then evaluate fg and f for the given value of. g. f ; g ; 8 f g ; ; f g 0 ; ;. In Eercises and 7, use a graphing calculator to evaluate ( f + g), ( f g), f ( fg)( ), and g when. Round our answers to two decimal places.. f ; g Describe and correct the error in stating the domain. f ; g In Eercises and 7, use a graphing calculator to evaluate ( f + g), ( f g), f ( fg)( ), and g when. Round our answers to two decimal places.. f ; g Describe and correct the error in stating the domain. f ; g f + and g The domain of ( f + g) is all real numbers. The domain of is all real numbers. 9. The growth of mold in Specimen A can be modeled b At () t. The growth of mold in Specimen B can be modeled b B () t t. a. Find ( A B)( t). b. Eplain what the function ( A B)( t) represents. 9. The table shows the outputs of the two functions f and g. Use the table to evaluate ( f + g)(, ) ( f f g)( 0, ) ( fg)(, ) and (. ) g 0 f() g() 8 8 Algebra Copright Big Ideas Learning, LLC 9

9 . Practice A. Practice B In Eercises, solve f for. Then find the input(s) when the output is.. f +. f. f 8 In Eercises, find the inverse of the function. Then graph the function and its inverse. f. f. f 7. Find the inverse of the function f b switching the roles of and and solving for. Then find the inverse of the function f b using inverse operations in the reverse order. Which method do ou prefer? Eplain. In Eercises, solve f for. Then find the input(s) when the output is.. f +. f. f In Eercises, find the inverse of the function. Then graph the function and its inverse. f +. f +. f 7. Describe and correct the error in finding the inverse function. 8. Determine whether each pair of functions f and g are inverses. Eplain our reasoning. a. b. 0 f() 9 0 g() 0 In Eercises 9, find the inverse of the function. Then graph the function and its inverse. 9. f 9, 0 0. f, 0. f ( + ) In Eercises and, use the graph to determine whether the inverse of f is a function. Eplain our reasoning.. 7. f() g() In Eercises 8 0, find the inverse function. Then graph the function and its inverse. 8. f 9, 0 9. f ( ) 0. f, 0. Find the inverse of the function f 8 b switching the roles of and and solving for. Then find the inverse of the function f b using inverse operations in the reverse order. Which method do ou prefer? Eplain. In Eercises, determine whether the functions are inverses. f g +. f + ; g. f ; g. f ; g ; 8 +. The volume of a sphere is given b V πr, where r is the radius. a. Find the inverse function. Describe what it represents. b. Find the radius of a sphere with a volume of cubic meters. 7 7 Algebra Copright Big Ideas Learning, LLC

10 . Practice A In Eercises, evaluate the epression for (a) and (b) Practice B In Eercises, evaluate the epression for (a) and (b) In Eercises 9, tell whether the function represents eponential growth or eponential deca. Then graph the function (.) In Eercises 0 and, use the graph of f b to identif the value of the base b. 0.. (, ) (, ) (0, ). The value of a rare coin (in dollars) can be approimated b the model t 0..0, where t is the number of ears since the coin was minted. a. Tell whether the model represents eponential growth or eponential deca. b. Identif the annual percent increase or decrease in the value of the coin. c. What was the original value of the coin? d. Estimate when the value of the coin will be $0.0. In Eercises, rewrite the function in the form t t a + r or a( r). Then state the growth or deca rate.. a() t a() t 8 (, 8 ) (0, ). a( 0.) t. You deposit $000 into a bank account that pas.% annual interest, compounded semi-annuall. How much interest does the account earn after ears? 8 (, 8) In Eercises 9, tell whether the function represents eponential growth or eponential deca. Then graph the function (.) 8. ( 0.) 9. In Eercises 0 and, use the graph of f b to identif the value of the base b The value of a truck (in dollars) can be approimated b the model t 0., , where t is the number of ears since the truck was new. a. Tell whether the model represents eponential growth or eponential deca. b. Identif the annual percent increase or decrease in the value of the truck. c. What was the original value of the truck? d. Estimate when the value of the truck will be $0,000. In Eercises, rewrite the function in the form t t a + r or a( r). Then state the growth or deca rate. a 0.7 t a 8. 8 (, 0) (, 0 ) (0, ) t (, ). a. You deposit $000 into a bank account that pas.% annual interest, compounded monthl. How much interest does the account earn after ears? (0, ) (, ) t 8 8 Algebra Copright Big Ideas Learning, LLC

11 . Practice A. Practice B In Eercises, simplif the epression. In Eercises, simplif the epression. 8. e e. e e. e e e e e 7 8e e. e e9 e Describe and correct the error in simplifing the epression. e 8 0e. 9 e. e e e 7. Describe and correct the error in simplifing the epression. ( e ) e In Eercises 8 0, tell whether the function represents eponential growth or eponential deca. Then graph the function. 8. e 9. e 0. e In Eercises, use the properties of eponents to rewrite the function in the form t t a + r or a( r). Then find the percent rate of change. 0.. e 0.. e 0.. e In Eercises, use a table of values or a graphing calculator to graph the function. Then identif the domain and range. e. e +. e + 7. You invest $000 in an account to save for college. a. Option pas % annual interest compounded semi-annuall. What would be the balance in the account after ears? b. Option pas % annual interest compounded continuousl. What would be the balance in the account after ears? c. At what time t (in ears) would Option give ou $00 more than Option? In Eercises 8 0, tell whether the function represents eponential growth or eponential deca. Then graph the function. 8. e 9. 0.e e In Eercises, use the properties of eponents to rewrite the function in the form t t a + r or a( r). Then find the percent rate of change e. e 0.9. e 0. In Eercises, use a table of values or a graphing calculator to graph the function. Then identif the domain and range. e. e. e + 7. You invest $000 in an account to save for college. a. Option pas % annual interest compounded monthl. What would be the balance in the account after ears? b. Option pas % annual interest compounded continuousl. What would be the balance in the account after ears? c. What is the difference between the two options after 0 ears? d. How would our answer to part (c) change if ou invested $0,000? 90 Algebra Copright Big Ideas Learning, LLC 9

12 Name. Practice A. Practice B In Eercises, rewrite the equation in eponential form.. log 8. log7 7. log In Eercises, rewrite the equation in logarithmic form. 0.. In Eercises 7, evaluate the logarithm. 7. log 8. log 9. log 0. log. log9. log 8 In Eercises, rewrite the equation in eponential form.. log9 0. log. log In Eercises, rewrite the equation in logarithmic form.. 9 In Eercises 7, evaluate the logarithm log8 8. log 9. log0 0. log. log 0.. log In Eercises, evaluate the logarithm using a calculator. Round our answer to three decimal places.. log ln. log. The decibel level D of sound is given b the equation 0 log I D, 0 where I is the intensit of the sound. What is the decibel level when the intensit of the 9 sound is 0? In Eercises 7 9, simpl the epression. log 7. log In Eercises 0, find the inverse of the function. log log. log ln. e. The wind speed s (in miles per hour) near the center of a tornado can be modeled b s 9 log d +, where d is the distance (in miles) that the tornado travels. a. A tornado traveled miles. Estimate the wind speed near the center of the tornado. b. The wind speed near the center of a tornado was 0 miles per hour. Find the distance that the tornado traveled. In Eercises, evaluate the logarithm using a calculator. Round our answer to three decimal places.. log ln(. ). ln 0.. The decibel level D of sound is given b the equation 0 log I D, 0 where I is the intensit of the sound. The pain threshold for sound is decibels. Does a sound with an intensit of 0 eceed the pain threshold? Eplain. In Eercises 7 9, simpl the epression. ln 7 log 8 7. e 8. In Eercises 0, find the inverse of the function log( 0 ) log. log. ln( ) + e. +. The length (in inches) of an alligator and its weight w (in pounds) are related b the function 7. ln w.8. a. Estimate the length (in inches) of an alligator that weighs 0 pounds. What is its length in feet? b. Find the inverse of the given function. Use the inverse function to find the weight of a -foot alligator. (Hint: Convert to inches first.) 9 9 Algebra Copright Big Ideas Learning, LLC

13 . Practice A. Practice B In Eercises 8, describe the transformation of f represented b g. Then graph each function.. f, g +. f e, g e., f g f e, g e +. f e, g e., f e g e 7., + f g( ) 8. f e, g e 9. Describe and correct the error in graphing the function f e. In Eercises 0 and, describe the transformation of f represented b g. Then graph each function. 0. f log, g log. f log, g log + In Eercises, write a rule for g that represents the indicated transformation of the graph of f.. f( ) ; reflection in the -ais, followed b a translation units left and unit down. f e ; vertical shrink b a factor of, followed b a translation units up f log ; reflection in the -ais, followed b a translation units left 8 f log ; vertical stretch b a factor of 9, followed b translations units (0, ) right and units down (, e ) (, e) In Eercises 8, describe the transformation of f represented b g. Then graph each function. +. f e, g e. f, g( ) f( ) g f e, g e., +. f, g. f e, g e + 8. f( ) g f e, g e Describe and correct the error in graphing the function, + + f. In Eercises 0 and, describe the transformation of f represented b g. Then graph each function. 0. f log, g log ( ) +. f log, g log ( ) In Eercises, write a rule for g that represents the indicated transformation of the graph of f. f ; reflection in the -ais, followed b a horizontal shrink b a factor of and a translation units down.. f e ; translation units left and units up, followed b a vertical stretch b a factor of f log ; translation units right and units down, followed b a reflection in the -ais 8 (0, ) (, ) (, 7) 00 Algebra Copright Big Ideas Learning, LLC 0

14 . Practice A In Eercises, use log 0.8 and log. to evaluate the logarithm.. log. log 8. log 9. Practice B In Eercises, use log 0.8 and log. to evaluate the logarithm.. log 8. log. log In Eercises, epand the logarithmic epression. log. log 7. log 7. Describe and correct the error in epanding the logarithmic epression. In Eercises, epand the logarithmic epression. 7 log. log. log8 7. Describe and correct the error in epanding the logarithmic epression. In Eercises 8, condense the logarithmic epression. 8. log7 log7 9. log 0 log 0. ln + 9 ln. log 9 + log In Eercises, use the change-of-base formula to evaluate the logarithm.. log. log log 0. Your friend claims that ou can use the change-of-base formula to write the epression ln as a common logarithm. Is our friend correct? Eplain our reasoning.. For a sound with intensit I (in watts per square meter), the loudness LI of the sound (in decibels) is given b the function LI 0 log I I, where I0 is the intensit of a barel audible sound (about 0 watts per square meter). The sound of a coach s whistle is five times greater than the intensit of the referee s whistle. Find the difference in the decibel levels of the sounds made b the coach and the referee. 0 In Eercises 8, condense the logarithmic epression. 8. log9 log9 9. log 8 + log8 0. ln + ln + ln. log 9 + log log In Eercises, use the change-of-base formula to evaluate the logarithm.. log8. log 0 log 8 7. Your friend claims ou can use the change-of-base formula to write the epression ln as a logarithm with base. Is our friend correct? Eplain our reasoning. ln. For a sound with intensit I (in watts per square meter), the loudness LI of the sound (in decibels) is given b the function LI 0 log I I, where I0 is the intensit of a barel audible sound ( about 0 watts per square meter ). 0 The bass guitar plaer in a band turns up the volume of the speaker so that the intensit of the sound triples. B how man decibels does the loudness increase? 0 0 Algebra Copright Big Ideas Learning, LLC

15 . Practice A. Practice B In Eercises, solve the equation e e The length (in centimeters) of a scalloped hammerhead shark can be modeled 0.0t b the function 9 e, where t is the age (in ears) of the shark. a. How old is a shark that is 00 centimeters long? In Eercises, solve the equation e + 0. e 7 7. Fift grams of radium are stored in a container. The amount R (in grams) of 0.000t radium present after t ears can be modeled b R 0 e. a. After how man ears will onl 0 grams of radium be present? 9 b. How long is a shark that is twice as old as the shark in part (a)? In Eercises 8, solve the equation. 8. ln( 8) ln( + ) 9. log ( 9 ) log ( + ) 0. log( + ) log. log +. log( 0 7). ( ) log + log In Eercises 7, solve the equation. Check for etraneous solutions. log + log ( ). ( ). ( ) log + log + ln + ln + 7. log + log 8. You deposit $00 in an account that pas % annual interest. How long will it take for the balance to double for each frequenc of compounding? a. annuall b. quarterl c. dail d. continuousl In Eercises 9, solve the inequalit < 0.. log > In Eercises and, use a graphing calculator to solve the equation.. ln +. log 9 b. Sevent-five grams of radium are stored in a different container. The amount R (in grams) of radium present after t ears can be modeled 0.000t b R 7e. Will it take more ears or fewer ears for onl 0 grams of the radium in this container to be present, compared to the answer in part (a)? Eplain. In Eercises 8, solve the equation. 8. ln( ) ln( + ) 9. log + log 0. log ( + ). log ( + 7) log ( 0). log ( + ). ( ) log In Eercises 7, solve the equation. Check for etraneous solutions. ( ) ln + ln. log + log 8. log ( ) + log ( + 8) 7. ( ) ( ) In Eercises 8 0, solve the inequalit. log + + log + 8. e < 8 9. ln > 0. log + 0. You deposit $000 in Account A, which pas.% annual interest compounded monthl. You deposit another $000 in Account B, which pas % annual interest compounded monthl. When is the sum of the balance in both accounts at least $000? 0 Algebra Copright Big Ideas Learning, LLC

16 7. Practice A 7. Practice B In Eercises, graph the function. Compare the graph with the graph of f.. h. g. h 9 In Eercises, graph the function. Compare the graph with the graph of f. 8. h. g. h 0. In Eercises, graph the function. State the domain and range. In Eercises, graph the function. State the domain and range. f +.. g f. g h h f g + 0. f +. g + 8. h h a In Eercises, rewrite the function in the form g + k. Graph the h a function. Describe the graph of g as a transformation of the graph of f.. g 9. g g 0. g g. g. Your choir is taking a trip. The trip has an initial cost of $00, plus $0 for each student. a. Estimate how man students must go on the trip for the average cost per student to fall to $7. b. What happens to the average cost as more students go on the trip? In Eercises, use a graphing calculator to graph the function. Then determine whether the function is even, odd, or neither. f. g +. h a In Eercises, rewrite the function in the form g + k. Graph the h a function. Describe the graph of g as a transformation of the graph of f.. g 9. g g 0. g g. g You are creating statues made of cement. The mold costs $00. The material for each statue costs $. a. Estimate how man statues must be made for the average cost per statue to fall below $0. b. What happens to the average cost as more statues are created?. The concentration c of a certain drug in a patient s bloodstream t hours after an t injection is given b ct (). t + a. Use a graphing calculator to graph the function. Describe a reasonable domain and range. b. Determine the time at which the concentration is the highest. Algebra Copright Big Ideas Learning, LLC

17 7. Practice A 7. Practice B In Eercises, simplif the epression, if possible. In Eercises, simplif the epression, if possible In Eercises 7, find the product ( + ) ( )( ) In Eercises 7, find the product. 7. ( ) ( + )( ) ( ) ( + 7)( ) Compare the function f In Eercises 7, find the quotient ( + )( ) to the function g. ( + ) ( + ) 8. Manufacturers often package products in a wa that uses the least amount of material. One measure of the efficienc of a package is the ratio of its surface area to its volume. The smaller the ratio, the more efficient the packaging. A compan makes a clindrical can to hold popcorn. The compan is designing a new can with the same height h and twice the radius r of the old can. S a. Write an epression for the efficienc ratio, where S is the surface area V of the can and V is the volume of the can. b. Find the efficienc ratio for each can. c. Did the compan make a good decision b creating the new can? Eplain ( 8 + ) In Eercises, find the quotient ( ) Find the ratio of the perimeter to the area of the square shown Find the epression that makes the following statement true ( + 9) Algebra Copright Big Ideas Learning, LLC

18 7. Practice A 7. Practice B In Eercises, find the sum or difference. In Eercises, find the sum or difference In Eercises 7, find the least common multiple of the epressions., 8., ( + ). 9, , + 8. Describe and correct the error in finding the sum. In Eercises 7, find the least common multiple of the epressions., , 0, , Describe and correct the error in finding and simplifing the sum In Eercises 9, find the sum or difference In Eercises and, tell whether the statement is alwas, sometimes, or never true. Eplain.. The LCD of two rational functions is the sum of the denominators. The LCD of two rational functions is equal to one of the denominators. a In Eercises 8, rewrite the function g in the form g + k. h Graph the function. Describe the graph of g as a transformation of the graph a of f.. g 7. g 0. g 8. g In Eercises 9, find the sum or difference In Eercises and, tell whether the statement is alwas, sometimes, or never true. Eplain.. The LCD of two rational functions is one of the denominators when the other denominator is a factor. The LCD of two rational functions will have a degree equal to that of the denominator with the higher degree. a In Eercises 8, rewrite the function g in the form g + k. h Graph the function. Describe the graph of g as a transformation of the graph a of f.. g + +. g 7. g 8. g Algebra Copright Big Ideas Learning, LLC

19 7. Practice A 7. Practice B In Eercises, solve the equation b cross multipling. Check our solution(s) In Eercises, solve the equation b cross multipling. Check our solution(s) So far in baseball practice, ou have pitched 7 strikes out of pitches. Solve the equation to find the number of consecutive strikes ou need to 00 + pitch to raise our strike percentage to 80%. In Eercises and, identif the least common denominator of the equation In Eercises 7, solve the equation b using the LCD. Check our solution(s) Describe and correct the error in the first step of solving the equation. So far in soccer practice, ou have made 0 out of goal attempts. Solve the 0 + equation 0. to find the number of consecutive goals ou need to + make to raise our goal average to 0.. In Eercises and, identif the least common denominator of the equation In Eercises 7, solve the equation b using the LCD. Check our solution(s) Describe and correct the error in the first step of solving the equation. You can clean the gutters of our house in hours. Working together, ou and our friend can clean the gutters in hours. Let t be the time (in hours) our friend would take to clean the gutters when working alone. Write and solve an equation to find how long our friend would take to clean the gutters when working alone. ( Hint: ( Work done) ( Work rate) ( Time) ) You can kaak around a certain island in hours. Kaaking together, ou and our friend can kaak around the island in. hours. Let t be the time (in hours) our friend would take to kaak around the island when kaaking alone. Write and solve an equation to find how long our friend would take to kaak around the island when kaaking alone. ( Hint: ( Work done) ( Work rate) ( Time) ) 7 8 Algebra Copright Big Ideas Learning, LLC

20 8. Practice A 8. Practice B In Eercises, write the first si terms of the sequence.. an n. an n. an n In Eercises, write the first si terms of the sequence.. an n +. an n. a ( n ) n an n. a n n. an n + In Eercises 7, describe the pattern, write the net term, and write a rule for the nth term of the sequence. 7.,, 7, 0, 8.,,9,7, 9..,,,, 0.,.8, 7., 9,. 7,.,., 0.8,., 0,, 0,.,,,,,,,, 8. You agree to work for our uncle. You earn $0 the first da, $0 the second da, $0 the third da, and $80 the fourth da. Write a rule for the number of dollars that ou will earn on the nth da. Then graph the sequence. In Eercises, write the series using summation In Eercises 7, find the sum.. i. i 7. ( n + ). ( k ) n i i 7. k n 0 n 7 i i 8. You are building a brick garden wall si rows high. The bottom row has bricks. Each of the other rows has three fewer bricks than the one below it. How man bricks will ou need to build the garden wall? Justif our answer. +. f( n) an n n n +. n an n In Eercises 7, describe the pattern, write the net term, and write a rule for the nth term of the sequence. 7., 7,, 7, 8..7,., 9.7,., 9..,., 0.,., 0.,,,, ,,,,., 9, 7, 8, 8.,, 8,,, 0, 00, 000, You are renting tables for a school event. There is a set-up and deliver fee of $00. The rental fee per table is $7. Write a rule for the cost of renting n tables. Then graph the sequence. In Eercises, write the series using summation In Eercises 7, find the sum... 9i. i. k + k i ( n + ) i 0 n 7. k 7 i 8. You are making part favors. In the first hour ou made part favors. Each hour ou make two more part favors than in the previous hour. How man part favors will ou have made after 7 hours? Justif our answer. i 9 0 Algebra Copright Big Ideas Learning, LLC

21 8. Practice A 8. Practice B In Eercises, tell whether the sequence is arithmetic. Eplain our reasoning..,,,, 7,. 9, 7,, 0,,.,,,,,,,9,7,8,. Write a rule for the arithmetic sequence with the given description. a. The first term is and each term is more than the previous term. b. The first term is 9 and each term is less than the previous term. In Eercises 9, write a rule for the nth term of the sequence. Then find a 0..,,9,, 7.,,,, 8., 0,, 0, 9.,, 0,, 0. Describe and correct the error in writing a rule for the nth term of the arithmetic sequence 7,,, 8,,. In Eercises, tell whether the sequence is arithmetic. Eplain our reasoning.. 00,0,,.,.,. 0,, 8,,,.,,,,,,, 9,,, 0 0. Write a rule for the arithmetic sequence with the given description. a. The first term is and each term is 7 less than the previous term. b. The first term is 8 and each term is 0 more than the previous term. In Eercises 9, write a rule for the nth term of the sequence. Then find a 0.. 7, 9,,, 7., 8,, 0, 8. 0.,.,,., 9..,., 0.8, 0., 0. Describe and correct the error in writing a rule for the nth term of the arithmetic sequence 7,,, 8,,. In Eercises and, write a rule for the nth term of the sequence. Then graph the first si terms of the sequence.. a9, d. a, d In Eercises, write a rule for the nth term of the sequence.. a 7, a0 a8 a, 9. a, a 8. a a 7, Find the sum of the positive even integers less than 0. Eplain our reasoning. In Eercises and, write a rule for the nth term of the sequence. Then graph the first si terms of the sequence.. a 07, d. a, d In Eercises, write a rule for the nth term of the sequence.. a, a9 9 a9 7, a 8. a, a 99. a a 8, 7. Find the sum of the positive odd integers less than 00. Eplain our reasoning. Algebra Copright Big Ideas Learning, LLC

22 8. Practice A 8. Practice B In Eercises, tell whether the sequence is geometric. Eplain our reasoning..,,, 8,,. 88,,,, 0,. 0.,.,.,,.9, 0.8, 8, 8.8, 7.8,. Write a rule for the geometric sequence with the given description. a. The first term is, and each term is times the previous term. b. The first term is, and each term is times the previous term. In Eercises 9, write a rule for the nth term of the sequence. Then find a 7..,,,, 7. 7,,, 89, 8. 9,9,8,, 9.,,,, In Eercises 0, write a rule for the nth term. Then graph the first si terms of the sequence. 0. a 9, r. a, r. a, r. a 08, r Describe and correct the error in writing a rule for the nth term of the geometric sequence for which a 7, r 7. In Eercises, tell whether the sequence is geometric. Eplain our reasoning..,, 8, 7, 0,.,,8,,,. 0.7,., 7., 87., 7.,, 0, 0, 0, 80,. Write a rule for the geometric sequence with the given description. a. The first term is, and each term is 7 times the previous term. b. The first term is, and each term is times the previous term. In Eercises 9, write a rule for the nth term of the sequence. Then find a 7.. 9, 8,, 7, 7. 80, 0,,, 8.,,,, 9..,.,8, 9., In Eercises 0, write a rule for the nth term. Then graph the first si terms of the sequence. 0. a 0, r. a 8, r. a 78, r. a, r Describe and correct the error in writing a rule for the nth term of the geometric sequence for which a 7, r 7. a n n a 7 7 n a r n. You are buing a new car. You take out a -ear loan for $0,000. The annual interest rate of the loan is %. You can calculate the monthl pament M (in dollars) for a loan using the formula M L, where L is the t k + i k loan amount (in dollars), i is the monthl interest rate (in decimal form), and t is the term (in months). Calculate the monthl pament.. You are buing a new boat. You take out a -ear loan for $0,000. The annual interest rate of the loan is %. You can calculate the monthl pament M (in dollars) for a loan using the formula M L, where L is the loan t k + i k amount (in dollars), i is the monthl interest rate (in decimal form), and t is the term (in months). Calculate the monthl pament Algebra Copright Big Ideas Learning, LLC

23 8. Practice A 8. Practice B In Eercises and, consider the infinite geometric series. Find the partial sums Sn for n,,,, and. Then describe what happens to S n as n increases. In Eercises and, consider the infinite geometric series. Find the partial sums Sn for n,,,, and. Then describe what happens to S n as n increases In Eercises, find the sum of the infinite geometric series, if it eists. n. 7 n n n In Eercises, find the sum of the infinite geometric series, if it eists. n. 7 n 7 n n Describe and correct the error in finding the sum of the infinite geometric series. 7. Describe and correct the error in finding the sum of the infinite geometric series. For this series, Because this series does not have a sum. For this series, 8. You push our ounger sister on a swing one time and then allow our sister to swing freel. On the first swing, our sister travels a distance of 8 feet. On each successive swing, our sister travels 80% of the distance of the previous swing. What is the total distance our sister swings? In Eercises 9, write the repeating decimal as a fraction in simplest form A compan had a profit of $00,000 in its first ear. Since then, the compan s profit has decreased b % each ear. Assuming this trend continues, what is the total profit the compan can make over the course of its lifetime? 8. You are going for a -mile run. You know that ou can run half the distance, and ou successfull run miles. There are miles to go, and ou know that ou can run half that distance. You successfull run that net mile. Now there is mile to go, and ou know that ou can run half that distance. You successfull run that net half mile. This process continues. Will ou cover the miles over the course of our run? Eplain our answer. In Eercises 9, write the repeating decimal as a fraction in simplest form A radio station has a dail contest in which a random listener is asked a trivia question. On the first da, the station gives $00 to the first listener who answers correctl. On each successive da, the winner receives 9% of the winnings from the previous da. What is the total amount of prize mone the radio station gives awa during the contest? 7 Algebra Copright Big Ideas Learning, LLC 7