assignment 4 multiple choice. choose the one alternative

Assignment 4Name___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the power function that the graph of f resembles for large values of |x|.

1) 1)f(x) = (x - 4)3

A) y = x3 B) y = x-4 C) y = x12 D) y = x-64

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

2) 2)f(x) = x(x - 15)

A) Yes; degree 1 B) Yes; degree 0

C) No; it is a product D) Yes; degree 2

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis ateach x -intercept.

3) 3)f(x) = 3(x2 + 1)(x2 + 3)2

A) -1, multiplicity 1, crosses x-axis; -3, multiplicity 2, touches x-axis

B) No real zeros

C) 1, multiplicity 1, crosses x-axis; -1, multiplicity 1, crosses x-axis;3, multiplicity 2, touches x-axis; - 3, multiplicity 2, touches x-axis

D) -1, multiplicity 1, touches x-axis; -3, multiplicity 2, crosses x-axis

4) f(x) =12

x4(x2 - 5)(x + 1) 4)

A) 0, multiplicity 4, crosses x-axis;-1, multiplicity 1, touches x-axis

B) 0, multiplicity 4, crosses x-axis;-1, multiplicity 1, touches x-axis;

5, multiplicity 1, touches x-axis;- 5, multiplicity 1, touches x-axis

C) 0, multiplicity 4, touches x-axis;-1, multiplicity 1, crosses x-axis;

5, multiplicity 1, crosses x-axis;- 5, multiplicity 1, crosses x-axis

D) 0, multiplicity 4, touches x-axis;-1, multiplicity 1, crosses x-axis

Find the power function that the graph of f resembles for large values of |x|.

5) 5)f(x) = (x + 5)2

A) y = x5 B) y = x2 C) y = x25 D) y = x10

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

6) f(x) =x3 - 4

x5 6)

A) Yes; degree -5 B) Yes; degree 5

C) Yes; degree 3 D) No; it is a ratio of polynomials

Use transformations of the graph of y = x4 or y = x5 to graph the function.

1

7) 7)f(x) = -2(x - 4)4 + 4

A) B)

C) D)

2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Analyze the graph of the given function f as follows:(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.(b) Graph f using a graphing utility.(c) Find the x- and y-intercepts of the graph.(d) Determine whether the graph crosses or touches the x-axis at each x-intercept.(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimalplaces.(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turningpoints.(g) Find the domain of f. Use the graph to find the range of f.(h) Use the graph to determine where f is increasing and where f is decreasing.

8) 8)f(x) = x2(x + 3)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use transformations of the graph of y = x4 or y = x5 to graph the function.

9) 9)f(x) = (x + 5)4

A) B)

3

C) D)

Find the x- and y-intercepts of f.

10) 10)f(x) = -x2(x + 4)(x2 + 1)

A) x-intercepts: -4, -1, 0; y-intercept: 4 B) x-intercepts: -4, -1, 0; y-intercept: -4

C) x-intercepts: -4, -1, 0, 1; y-intercept: 0 D) x-intercepts: -4, 0; y-intercept: 0

Use the graph to determine the domain and range of the function.

11) 11)

A) domain: {x|x 3}range: {y|y 0}

B) domain: {x|x > 0}range: {y|y 3}

C) domain: {x|x 0}range: {y|y 3}

D) domain: {x|x 3}range: {y|y > 0}

4

Use the graph to find the horizontal asymptote, if any, of the function.

12) 12)

A) y = 0 B) x = -1, x = 1, y = 0

C) y = -1, y = 1 D) none

Graph the function using transformations.

13) f(x) = 3 -1

(x + 6)213)

A) B)

5

C) D)

Give the equation of the horizontal asymptote, if any, of the function.

14) H(x) =25x5 - 5x - x3 14)

A) y = -25 B) y = -1, y = 1 C) y = 0 D) none

15) F(x) =x2 - 7

49x - x4 15)

A) y = -1 B) y = -7, y = 7 C) y = 0 D) none

16) G(x) =x2 + 1x - 8

x - 816)

A) y = 0 B) y = 1 C) y = 8 D) none

Graph the function using transformations.

17) f(x) =1x

- 3 17)

6

A) B)

C) D)

Give the equation of the horizontal asymptote, if any, of the function.

18) Q(x) =x + 9

x2 - 2518)

A) y = 1 B) y = -5, y = 5 C) y = 0 D) none

Find the domain of the rational function.

19) R(x) =x + 6x2 - 9

19)

A) {x|x -3, x 3} B) {x|x 0, x 9}

C) {x|x -3, x 3, x -6} D) all real numbers

20) G(x) =x

x3 - 12520)

A) {x|x 5} B) {x|x -5} C) {x|x 25} D) {x|x -5, 5}

Find the indicated intercept(s) of the graph of the function.

21) y-intercept of f(x) = x +49x 21)

A) (0, 0) B) (0, 7) C) (0, 49) D) none

7

22) y-intercept of f(x) =8

x2 - 3x - 2322)

A) 0, 823 B) (0, 8) C) 0, -

823 D) none

Solve the problem.

23) 23)The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled

by the function, C(t) =12t + 43t2 + 2

, where t is the number of minutes after injection of the drug. When

will the drug be at its highest concentration? Approximate your answer rounded to two decimalplaces.

A) at the time of injection

B) t = 3.65 minutes after the injection is given

C) t = 0.55 minutes after the injection is given

D) t = 4 minutes after the injection is given

Graph the function.

24) f(x) =x2 - 5x + 4

(x - 5)224)

A) B)

8

C) D)


25) x-intercepts of f(x) =x - 4

x2 + 6x - 225)

A) (6, 0) B) (-4, 0) C) (4, 0) D) none

Graph the function.

26) f(x) =x4

x2 + 2526)

A) B)

9

C) D)

Solve the problem.

27) 27)A closed box with a square base has to have a volume of 4000 cubic inches. Find a function for thesurface area of the box.

A) S(x) = 2x2 +24,000

x B) S(x) = 2x2 +16,000

x

C) S(x) = 2x2 +4000

x D) S(x) = x2 +16,000

x

Graph the function.

28) f(x) =x4 - 1

x2 - 8128)

10

A) B)

C) D)


29) y-intercept of f(x) =(x - 8)2

(x + 11)329)

A) 0, -8

11 B) 0, -64

1331 C) 0, 641331 D) (0, 8)

Graph the function.

11

30) f(x) = x +1x 30)

A) B)

C) D)

Solve the problem.

31) 31)Suppose that the daily cost C of manufacturing x bicycles is given by C(x) = 80x + 7000. Then the

average daily cost C is given by C(x) =80x + 7000

x. How many bicycles must be produced each day

in order for the average cost to be no more than $150?

A) {x|x 10}; [10, ) B) {x|x 1000}; [1000, )

C) {x|x 100}; [100, ) D) {x|0 < x 100}; (0, 100]

12

Solve the inequality by using the graph of the function.

32) 32)f(x) > 0, where f(x) = -x(x + 1)(x - 2)(x - 3).

A) (- , -1) (0, 2) B) (2, 3) C) (-1, 0) (2, ) D) (-1, 0) (2, 3)

33) 33)f(x) < 0, where f(x) = (x + 3)(x + 2)(x - 3).

A) (- , -3) (-2, 3) B) (-2, 3)

C) (- , -3) (-2, ) D) (-3, -2) (3, )

Solve the problem.

34) What is the domain of the function f(x) =x - 3x + 8

? 34)

A) [3, ) B) ( , -8) [3, ) C) ( , -8) D) ( , -8) (3, )

Solve the inequality algebraically. Express the solution in interval notation.

35) (x - 7)(x + 7)x

0 35)

A) (- , -7] (0, 7] B) [-7, 0) [7, ) C) [-7, 0) (0, 7] D) (- , -7] [7, )

13

36) (8 - x)3(8x - 3)x3 + 8

< 0 36)

A) 38

, 2 (8, ) B) -8, 38

(2, ) C) (-2, 8) 38

, D) -2, 38

(8, )

Solve the problem.

37) 37)What is the domain of the function f(x) = x4 - 16 ?

A) ( , 2) (2, ) B) ( , -2] [2, ) C) ( , -2) (2, ) D) ( , 2)


38) 38)x4 - 21x2 - 100 > 0

A) (- , -5) (5, ) B) (- , -5) (-2, 2) (5, )

C) (-5, 5) D) (-5, -2) (2, 5)

Solve the inequality by using the graph of the function.

39) f(x) < 0, where f(x) =-4

(x - 1)(x + 5). 39)

A) (- , -5] [1, ) B) [-5, 1] C) (-5, 1) D) (- , -5) (1, )


40) 9x - 3x + 8

8 40)

A) (-8, 67) B) (-8, 11) C) (-8, 67] D) (-8, 11]

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in theform f(x) = (x - c)(quotient).

41) 41)f(x) = 4x3 + 41x2 + 53x + 72; x + 9

A) Yes; f(x) = (x - 9)(4x2 + 5x - 8) B) Yes; f(x) = (x + 9)(4x2 + 5x + 8)

C) No D) Yes; f(x) = (x + 9)(4x2 + x + 8)

Find the real solutions of the equation.

42) 42)x3 + 7x2 - 16x + 18 = 0

A) {9} B) {-9} C) {-9, 9} D) {1}

14

Use the Factor Theorem to determine whether x - c is a factor of f(x).

43) 43)3x3 + 13x2 - 9x + 5; x + 5

A) Yes B) No

44) 44)5x4 + 19x3 - 4x2 + x - 4; x + 4

A) Yes B) No

Find the real solutions of the equation.

45) 45)x4 - 8x3 + 16x2 + 8x - 17 = 0

A) {-4, 1} B) {-1, 1} C) {-1, 4} D) {-4, 4}

Find the intercepts of the function f(x).

46) 46)f(x) = 3x3 - x2 - 15x + 5

A) x-intercepts: 3, 5, - 5; y-intercept: 5

B) x-intercepts: -13

, 5, - 5; y-intercept: 5

C) x-intercepts: -3, 5, - 5; y-intercept: 5

D) x-intercepts: 13

, 5, - 5; y-intercept: 5

Use the Factor Theorem to determine whether x - c is a factor of f(x).

47) 47)f(x) = x3 + 2x2 - 6x + 8; x + 4

A) Yes B) No


48) 48)f(x) = x3 + 3x2 - 4x - 12

A) x-intercept: -3; y-intercept: -12 B) x-intercept: -2; y-intercept: -12

C) x-intercepts: -2, 2, 3; y-intercept: -12 D) x-intercepts: -3, -2, 2; y-intercept: -12

List the potential rational zeros of the polynomial function. Do not find the zeros.

49) 49)f(x) = -2x3 + 4x2 - 3x + 8

A) ± 18

, ± 14

, ± 12

, ± 1, ± 2, ± 4, ± 8 B) ± 12

, ± 1, ± 2, ± 4

C) ± 12

, ± 1, ± 2, ± 4, ± 8 D) ± 14

, ± 12

, ± 1, ± 2, ± 4, ± 8


50) 50)f(x) = (x + 1)(x - 7)(x - 1)2

A) x-intercepts: -1, 1, -7; y-intercept: 7 B) x-intercepts: -1, 1, -7; y-intercept: -7

C) x-intercepts: -1, 1, 7; y-intercept: -7 D) x-intercepts: -1, 1, 7; y-intercept: 7

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assignment 4 multiple choice. choose the one alternative

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