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8/14/2019 Review Name

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REVIEW

Name___________________________________

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

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

1) 1)f(x) = 13x3 - 5x2 - 6

A) Yes; degree 5 B) Yes; degree 3

C) Yes; degree 6 D) No; the last term has no variable

2) f(x) =4

3-

1

4x 2)

A) Yes; degree 0 B) Yes; degree 4

C) Yes; degree 1 D) No; x has a fractional coefficient

3) 3)6(x - 1)11(x + 1)5

A) Yes; degree 66 B) Yes; degree 11 C) Yes; degree 16 D) Yes; degree 6

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Form a polynomial whose zeros and degree are given.

4) 4)Zeros: - 1, 1, - 6; degree 3

A) f(x) = x3 - 6x2 + x - 6 for a = 1 B) f(x) = x3 + 6x2 + x + 6 for a = 1

C) f(x) = x3 - 6x2 - x + 6 for a = 1 D) f(x) = x3 + 6x2 - x - 6 for a = 1

5) 5)Zeros: 3, multiplicity 2; - 3, multiplicity 2; degree 4

A) f(x) = x4 - 6x3 + 18x2 - 27x + 81 B) f(x) = x4 + 18x2 + 81

C) f(x) = x4 + 6x3 - 18x2 + 27x - 81 D) f(x) = x4 - 18x2 + 81

For the polynomial, li st each real zero and its multiplicity. Determine whether the graph crosses or touches the x- axis at

each x - intercept.

6) 6)f(x)=

5(x2 +

3)(x+

2)2

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

B) - 2, multiplicity 2, touches x- axis

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

D) - 2, multiplicity 2, crosses x- axis

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7) f(x) = x +1

2

2(x2 + 9)3 7)

A)1

2, multiplicity 2, touches x- axis; 9, multiplicity 3, crosses x- axis

B) -1

2, multiplicity 2, crosses x - axis

C) -1

2, multiplicity 2, touches x- axis

D) -1

2, multiplicity 2, touches x- axis; - 9, multiplicity 3, crosses x- axis

8) f(x) =1

2x4(x2 - 5) 8)

A) 0, multiplicity 4, crosses x- axis B) 0, multiplicity 4, crosses x- axis;

5, multiplicity 1, touches x- axis;

- 5, multiplicity 1, touches x- axis

C) 0, multiplicity 4, touches x- axis D) 0, multiplicity 4, touches x- axis;

5, multiplicity 1, crosses x- axis;

- 5, multiplicity 1, crosses x- axis

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9) 9)f(x) = 4(x - 7)(x - 5)4

A) 7, multiplicity 1, touches x- axis; 5, multiplicity 4, crosses x- axis

B) 7, multiplicity 1, crosses x- axis; 5, multiplicity 4, touches x- axis

C) - 7, multiplicity 1, touches x- axis; - 5, multiplicity 4, crosses x- axis

D) - 7, multiplicity 1, crosses x- axis; - 5, multiplicity 4, touches x- axis

10) f(x) =1

4x2(x2 - 5)(x + 5) 10)

A) 0, multiplicity 2, crosses x-

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

5, multiplicity 1, touches x- axis;


B) 0, multiplicity 2, touches x-

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

C) 0, multiplicity 2, touches x- axis;

- 5, multiplicity 1, crosses x- axis;

5, multiplicity 1, crosses x- axis;

- 5, multiplicity 1, crosses x- axis

D) 0, multiplicity 2, crosses x- axis;


Find the x- and y- intercepts of f.

11) 11)f(x) = 2x3(x - 2)5

A) x- intercepts: 0, 2; y- intercept: 2 B) x- intercepts: 0, - 2; y- intercept: 2

C) x- intercepts: 0, 2; y- intercept: 0 D) x- intercepts: 0, - 2; y- intercept: 0

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

12) 12)f(x) = - x2(x + 9)3(x2 - 1)

A) y = x7 B) y = - x7 C) y = x5 D) y = x6

Perform the indicated operation and show all necessary work to receive full credit.

Solve the problem.

13) 13)The price p and x, the quantity of a certain product sold, obey the demand equation

p = -1

10x + 100, {x|0 x 1000}

a) Express the revenue R as a function of x.b) What is the revenue if 450 units are sold?

c) Graph the revenue function using a graphing utility.

d) What quantity x maximizes revenue? What is the maximum revenue?

e) What price should the company charge to maximize revenue?

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Analyze the graph of the given function f as follows:

a) Find the x- and y- intercepts of the graph of f . Round to two decimal places, if necessary.

b) Determine whether the graph crosses or touches the x- axis at each x- intercept.

c) End behavior: find the power function that the graph of f resembles for large values of |x|.

d) Use a graphing utility to graph the function. Approximate the local maxima rounded to two decimal places, if

necessary. Approximate the local minima rounded to two decimal places, if necessary.

e) Determine the number of turning points on the graph.

f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f .

14) 14)f(x) = (x - 2)3(x - 3)2(x - 4)

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15) 15)f(x) = x3 - 4x + 2

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

Solve the problem.

16) 16)Let P = (x, y) be a point on the graph of y = x. Express the distance d from P to the point (1, 0) as a

function of x.

A) d(x) = x2 - x + 1 B) d(x) = x2 + 2x + 2

C) d(x) = x2 + 2x + 2 D) d(x) = x2 - x + 1

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17) 17)Bob wants to fence in a rectangular garden in his yard. He has 70 feet of fencing to work with and

wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x.

A) A(x) = 35x - x2 B) A(x) = 36x - x2 C) A(x) = 34x - x2 D) A(x) = 37x2 - x

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