Review - Test #3

Name___________________________________

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

Use the equation and the corresponding graph for the quadratic function to find what is requested.1) f(x) = (x - 2)2 - 5

Find the domain and range.

Match the equation to the correct graph.

2) y = -12

(x + 5)2 - 2

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

Find the domain and range of the function.3) f(x) = 5x2 - 100x + 502

A) Domain: (- , ); Range: (- , 10] B) Domain: (- , ); Range: [2, )C) Domain: (- , ); Range: (- , 0] D) Domain: (- , ); Range: [0, )

Find the equation of the axis of symmetry of the parabola.4) y = 3x2 + 30x + 73

A) x = 5 B) x = 2 C) x = -2 D) x = -5

Identify the vertex of the parabola.5) y = 4x2 - 40x + 96

A) (-4, 5) B) (4, -5) C) (5, -4) D) (-5, 4)

6) f(x) = -9(x + 7)2 + 1A) (-7, -1) B) (-7, 1) C) (7, 1) D) (-63, 1)

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

Sketch the graph of the parabola.7) y = 3(x - 4)2 - 6

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

Given the equation or other information for a parabola, find the matching description or graph.8) f(x) = ax2 + bx + c,

a < 0; b2 - 4ac = 0A) B)

C) D)

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9) f(x) = ax2 + bx + c,a < 0; b2 - 4ac = 0

A) B)

C) D)

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10) f(x) = ax2 + bx + c,a > 0; b2 - 4ac < 0

A) B)

C) D)

Use synthetic division to perform the division.

11) -5x3 - 33x2 - 12x + 36x + 6

A) -56

x2 + -112

x + - 2 B) -5x - 3

C) -5x2 - 3x + 6 D) 5x2 - 6x + 6

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.12) f(x) = 2x4 - x3 - 15x2 + 3x; k = -3

A) f(x) = (x - 3)(2x3 -7x2 + 6x - 15) + 45 B) f(x) = (x - 3)(2x3 - 5x2 + 3) + 9C) f(x) = (x + 3)(2x3 + 5x2 + 3) + 9 D) f(x) = (x + 3)(2x3 - 7x2 + 6x - 15) + 45

Use the remainder theorem and synthetic division to find f(k).13) k = -3; f(x) = 2x3- 5x2 - 4x + 17

A) -94 B) -70 C) -38 D) -6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.14) 3; f(x) = -x4 + 4x2 - x + 1

A) Yes B) No

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Use the factor theorem to decide whether or not the second polynomial is a factor of the first.15) 8x3 + 36x2 - 19x + 5; x + 5

A) Yes B) No

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

Sketch the graph of the parabola.

16) y = -12

(x - 2)2 - 3

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

Factor f(x) into linear factors given that k is a zero of f(x).17) f(x) = x4 + 10x3 + 13x2 - 120x - 300; k = -5 (multiplicity 2)

A) f(x) = (x + 5)2(x - 12)(x + 12) B) f(x) = (x + 5)2(x - 12)(x + 12)C) f(x) = (x -5) (x + 5) (x - 12)(x + 12) D) f(x) = (x -5 )2(x - 12)(x + 12)

For the polynomial, one zero is given. Find all others.18) P(x) = x3 - 3x2 - 5x + 39; -3

A) 1 + 2 13i, 1 - 2 13i B) 3 + 2i, 3 - 2iC) 1 + 2i, 1 - 2i D) 3 + 4i, 3 - 4i

Give all possible rational zeros for the following polynomial.19) P(x) = 3x3 + 32x2 + 32x + 27

A) ±1, ±3, ±9, ±27 B) ±1, ±1/3, ±3, ±9, ±27C) ±1, ±1/3, ±1/9, ±1/27, ±3 D) ±1, ±3, ±6, ±9, ±27

Find all rational zeros and factor f(x).20) f(x) = 4x3 - 28x2 - x + 7

A) 12

, - 12

, 7; f(x) = (2x - 1)(2x + 1)(x - 7) B) 2, -2, 7; f(x) = (x - 2)(x + 2)(x - 7)

C) 1, -1, 7; f(x) = (2x - 1)(2x + 1)(x - 7) D) 12

, - 12

, 7; f(x) = (x - 2)(x + 2)(x - 7)

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Find the zeros of the polynomial function and state the multiplicity of each.21) f(x) = (x2 + 14x + 45)2

A) 5, multiplicity 2; - 5, multiplicity 2 B) - 5, multiplicity 4C) 9, multiplicity 2; 5, multiplicity 2 D) -5, multiplicity 2; -9, multiplicity 2

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.22) Zeros of -2, 1, 0 and P(2) = 32

A) P(x) = 4x3 - 4x2 - 8x B) P(x) = 4x2 + 4x - 8C) P(x) = 4x3 + 12x2 - 8x D) P(x) = 4x3 + 4x2 - 8x

Find a polynomial of lowest degree with only real coefficients and having the given zeros.23) - 7, 7, and -3i

A) f(x) = x4 + 4x2 + 63 B) f(x) = x4 + 2x2 - 63 C) f(x) = x4 - 4x2 + 63 D) f(x) = x4 - 2x2 - 63

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negativereal zeros for the function.

24) 3x6 - 6x4 - 3x3 + 3x2 - 2x = 0A) Positive (3, 1), negative (2, 0) B) Positive (2, 0), negative (0)C) Positive (2, 0), negative (3, 1) D) Positive (3, 1), negative (2)

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.25) f(x) = x3 - 2x2 - 11x + 52

A) -4, 3 + 4i, 3 - 4i B) -4, 1 + 2 13i, 1 - 2 13iC) -4, 3 + 2i, 3 - 2i D) -4, 1 + 2i, 1 - 2i

Find the correct end behavior diagram for the given polynomial function.26) P(x) = -x5 - 7x3 - 4x + 1

A) B) C) D)

27) P(x) = 4 - 4x + x2 - x3 - 4x4A) B) C) D)

28) P(x) = 3x7 + 2x2 - 8A) B) C) D)

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

Graph the polynomial function. Factor first if the expression is not in factored form.29) f(x) = -3x(x + 1)2

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

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

A) B)

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C) D)

Use the graph to answer the question.31) Find the domain and range of the rational function graphed below.

A) Domain: (- , ); Range: (- , 1) (1, )B) Domain: (- , 1) (1, ); Range: (- , -4) (-4, )C) Domain: (- , -4) (-4, ); Range: (- , 1) (1, )D) Domain: (- , -4) (-4, ); Range: (- , )

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

Give the domain and range for the rational function. Use interval notation.

32) f(x) = -1

(x - 3)2+ 5

33) f(x) = 1x + 5

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

Find any vertical asymptotes.

34) h(x) = (x - 9)(x + 4)x2 - 9

A) None B) x = 9, x = -4 C) x = -9, x = 4 D) x = 3, x = -3

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Find the horizontal asymptote of the given function.

35) g(x) = x2 + 8x - 5x - 5

A) y = - 5 B) None C) y = 8 D) y = 0

36) h(x) = 4 - 9x- 3x + 7

A) y = - 3 B) y = 3 C) None D) y = 0

Give the equation of the oblique asymptote, if any.

37) f(x) = x2 + 2x - 3x - 4

A) None B) x = y + 6 C) y = x + 6 D) y = x - 2

Solve the inequality. Write the solution set in interval notation.38) (x + 6)(x - 2)(x - 9) < 0

A) (- , -6) (2, 9) B) (9, ) C) (-6, 2) (9, ) D) (- , 2)

Solve the rational inequality. Write the solution set in interval notation.

39) 5x-3x + 14

15

A) 215

, 143

B) - , 0 143

, C) - , 215

215

, D) 0, 143

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Sketch the graph of the rational function.

40) f(x) = x - 2x + 3

A) B)

C) D)

Solve the quadratic inequality. Write the solution set in interval notation.41) x2 + 4x + 3 > 0

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

Solve the inequality. Write the solution set in interval notation.42) x3 + 3x2 - 9x 27

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

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

Sketch the graph of the rational function.

43) f(x) = x2 - 9x - 3

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

Solve the rational inequality. Write the solution set in interval notation.

44) x - 7x + 8

0

A) [-7, 8] B) (-8, 7] C) (-7, 8] D) [-8, 7]

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

Sketch the graph of the rational function.

45) f(x) = x + 2x2 - 16

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

Solve the quadratic inequality. Write the solution set in interval notation.46) x2 + 7x -12

A) [3, 4] B) (- , 3] [4, ) C) [-4, -3] D) (3, 4)

Solve the inequality. Write the solution set in interval notation.47) x3 + 4x2 - 4x - 16 0

A) [-4, 2] B) [-4, -2] [2, ) C) [-4, ) D) [-2, 2] [4, )

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Answer KeyTestname: TEST 3- REVIEW

1) Domain: ( , ); Range: [-5, )2)

3) B4) D5) C6) B7)

8) C9) D

10) C11) C12) D13) B14) B15) A

16)

17) B18) B19) B20) A21) D22) D23) B24) A25) C26) B27) D28) D29)

30) D31) C32) Domain: (- , 3) (3, ); Range:

(- , 5)33) Domain: (- , -5) (-5, );

Range: (- , 0) (0, )34) D35) B36) B37) C38) A39) A

40) A41) D42) C43)

44) B45)

46) C47) B

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