End of Chapter Test. b. What are the roots of this equation? 8 1 x x 5 0

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1 End of Chapter Test Name Date 1. A woodworker makes different sizes of wooden blocks in the shapes of cones. The narrowest block the worker makes has a radius r 8 centimeters and a height h centimeters. For each centimeter increase in the radius, the worker decreases the height of the cone four centimeters. a. The volume of each wooden cone is represented b the formula V 1 3 p(radius) (height). Let represent the number of centimeters b which the worker increases the radius. Write a function V() to represent the volume of each cone the worker makes as a function of. V() 1 3 p(8 1 ) ( ) h r b. What are the roots of this equation? The equation has a double root at 8 and a root at 11. c. What is the domain that makes sense for this for this problem? Eplain our reasoning. The minimum value is 0 because it gives the maimum height of the cone. However, #. in order for the height to be greater than zero. d. Calculate the volume for each integer value of in this domain. Organize our results in a table. Round to the nearest integer V() e. For what integer value of is the volume of the cone a maimum? The volume of the cone is a maimum when 1. f. What is the maimum volume of the cone? The maimum volume of the cone is 17 cubic centimeters. Chapter Assessments 1003

2 End of Chapter Test page. Describe the end behavior of the function r() As `, r() `. As `, r() `. 3. Determine the product, h(), of the linear and quadratic factors. f() 7 3 and g() 1 3 h() f()? g() (7 3)( 1 3) The function b() is shown. Graph and label the function c() 8 on the same coordinate plane. b() 8 6 c() State whether the graph represents a function that is even, odd, or neither. Eplain our reasoning. The function is neither even nor odd because the graph is not smmetric about the origin nor is it smmetric about the -ais Chapter Assessments

3 End of Chapter Test page 3 Name Date 6. The graph of the basic cubic function v() 3 is shown. Suppose that w() v(). Use reference points and smmetr to complete the table of values for w(). Then, graph w() on the same coordinate plane as k() and label it. Reference Points on v() Corresponding Points on w() (0, 0) (0, ) (1, 1) (1, ) (, 8) (, 1) 8 6 v() w() 7. The functions f() and g() 3 are shown. Consider the function h() f() 3g() 1. Complete the table of values and sketch h() on the coordinate plane. f() g() h() f() g() h() Chapter Assessments 100

4 End of Chapter Test page 8. List the possible number of etrema for each tpe of polnomial. a. th degree polnomial: 0,, and b. 6th degree polnomial: 1, 3, and 9. Scientists recorded the population of beetles in an area during a 9-month period. The data from the stud was plotted, and a quartic regression was used to generate the polnomial function to best represent the data a. During what month(s) of the stud were there the most beetles, and approimatel how man beetles were there? The most beetles were recorded in month 3. There were approimatel 10,000 beetles. b. During what month(s) of the stud were the number of beetles predicted b the function unreasonable? Eplain our reasoning. The number predicted during months to 9 is unreasonable because there cannot be a negative number of beetles. c. During which months were the number of beetles increasing? The number of beetles was increasing between month 8 and month Chapter Assessments

5 End of Chapter Test page Name Date 10. Sketch the basic shape of each function on the set of aes, given the number of zeros of the function. a. Quartic polnomial with eactl 3 zeros b. Quintic polnomial with eactl zeros 11. Sketch the graph of the cubic function that is the product of the functions shown. a. b Show that the functions f() and g() are closed under addition Chapter Assessments 1007

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7 Standardized Test Practice Name Date 1. Determine the product, h(), of the given linear and quadratic factors. f() 1 and g() 3 1 a. h() b. h() c. h() d. h() Analze the given table. s() t() p() s() * t() How man real and imaginar roots does p() have? a. 1 real root; 0 imaginar roots b. 1 real root; imaginar roots c. real roots; 0 imaginar roots d. real roots; imaginar roots 3. Which is a characteristic of all cubic functions? a. The are alwas increasing. b. The have at least 1 -intercept. c. The have eactl relative etrema. d. The are smmetric about the origin.. Which is a possible number of etrema for a th degree polnomial? a. 0 b. 1 c. 3 d. Chapter Assessments 1009

8 Standardized Test Practice page. Which graph could represent the function f() 3 1? a. b. c. d. 6. Reflect the function f() about the -ais and translate it 3 units to the left to produce g(). Which equation represents the function g()? a. g() 1 3 b. g() 3 c. g() ( 3) d. g() ( 1 3) 1010 Chapter Assessments

9 Standardized Test Practice page 3 Name Date 7. Which could be the graph of r() ( 1 )( 1)? a. b. c. d. 8. Which function is even? a b c. 9 1 d Which function is equivalent to f() ? a. f() ( 1 3 1)(3 1) b. f() (3 1)( 1 1) c. f() (3 1 1)( 1) d. f() ( 1)(3 1 1) Chapter Assessments 1011

10 Standardized Test Practice page 10. Consider the table of values, where d() k() 1 m() 3. k() m() d() What is the specific equation for d()? a. d() b. d() c. d() d. d() A compan makes different sizes of boes. The widest bo has a width, w, of 7 inches, a depth d of 10 inches, and a height, h, of 8 inches. Other boes the compan makes decrease in width b increments of 3 inches. For each decrease of 3 inches in width, however, both d and h increase b 1 inch. w d h Which function represents the volume of each bo the compan makes? a. V() (7 3)(10 1 1)(8 1 1) b. V() (3 7)(1 1 10)(1 1 8) c. V() (3 7)( 1 10)( 1 8) d. V() (7 3)(10 1 )(8 1 ) 1. Which tpe of polnomial could a graph with the given shape represent? a. 3rd degree polnomial b. th degree polnomial c. th degree polnomial d. 6th degree polnomial 101 Chapter Assessments

11 Standardized Test Practice page Name Date 13. Which statement describes the polnomials and 6 1? a. The are closed under both multiplication and division. b. The are not closed under either multiplication or division. c. The are closed under multiplication but not closed under division. d. The are closed under division but not closed under multiplication. 1. The graph shown represents the function h() p() q() r(). 8 h() 0 8 Which functions could be p(), q(), and r()? a. p() 1 ; q() 1 1; r() 1 b. p() ; q() 1 1; r() 1 1 c. p() ; q() 3 1 1; r() d. p() 1 ; q() 3 1; r() 1 1. The volume V() of a bo is defined b the function V() (16 )(18 ), where each factor represents a dimension of the bo. What is the domain of the function for this problem situation? a. 0, # b. 0, #. c., # 16 d.., # The equation for f() is given. The equation for the transformed function g() in terms of f() is also given. Describe the transformation(s) performed on f() that produced g(). f() ; g() f( 3) a. stretched verticall b a factor of ; shifted 3 units to the left b. stretched verticall b a factor of ; shifted 3 units to the right c. shrunk verticall b a factor of ; shifted 3 units to the left d. shrunk verticall b a factor of ; shifted 3 units to the right Chapter Assessments 1013

12 Standardized Test Practice page Which graph represents a function that is neither even nor odd? a. b. 0 0 c. d Consider the graph shown. Which function could this graph represent? a. An odd-degree function with two relative etrema b. An even-degree function with two relative etrema c. An odd-degree function with three relative etrema d. An even-degree function with three relative etrema 101 Chapter Assessments

13 Standardized Test Practice page 7 Name Date 19. What is the end behavior of the function f() ? a. As `, f() `, and as `, f() `. b. As `, f() `, and as `, f() `. c. As `, f() `, and as `, f() `. d. As `, f() `, and as `, f() `. 0. Analze the graph. 0 Which functions could ou multipl to get a function that the graph represents? a. h() 1 and k() b. h() 1 and k() 1 3 c. h() 1 3 and k() d. h() 3 and k() 1 Chapter Assessments 101

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