C H A P T E R 2 Polynomial and Rational Functions

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262 Chapter 2 Polynomial and Rational Functions Chapter 2 Practice Test 1. Sketch the graph of f x x and identify the vertex and the intercepts. 2 6x 5 2. Find the number of units x that produce a minimum cost C if C 0.01x 2 90x 15,000. 3. Find the quadratic function that has a maximum at 1, 7 and passes through the point 2, 5. 4. Find two quadratic functions that have x-intercepts and 4 2, 0 , 0. 5. Use the leading coefficient test to determine the right and left end behavior of the graph of the polynomial function fx 3x 5 2x 3 17. 6. Find all the real zeros of f x x 5 5x 3 4x. 7. Find a polynomial function with 0, 3, and 2 as zeros. 8. Sketch f x x 3 12x. 9. Divide 3x using long division. 4 7x 2 2x 10 by x 3 10. Divide x 3 11 by x 2 2x 1. 11. Use synthetic division to divide 3x 5 13x 4 12x 1 by x 5. 12. Use synthetic division to find f6 given fx 7x 3 40x 2 12x 15. 13. Find the real zeros of fx x 3 19x 30. 14. Find the real zeros of fx x 4 x 3 8x 2 9x 9. 15. List all possible rational zeros of the function fx 6x 3 5x 2 4x 15. 16. Find the rational zeros of the polynomial fx x 3 20 3 x2 9x 10 3 . 17. Write fx x as a product of linear factors. 4 x3 5x 10 18. Find a polynomial with real coefficients that has 2, 3 i, and 3 2i as zeros. 3
19. Use synthetic division to show that 3i is a zero of fx x 3 4x 2 9x 36. x 1 20. Sketch the graph of fx and label all intercepts and asymptotes. 2x 21. Find all the asymptotes of fx 8x2 9 x 2 1 . 22. Find all the asymptotes of fx 4x2 2x 7 . x 1 23. Given z1 4 3i and z 2 2 i, find the following: (a) z1 z2 (b) z 1 z 2 (c) z 1z 2 24. Solve the inequality: x 2 49 ≤ 0 25. Solve the inequality: x 3 ≥ 0 x 7 Practice Test for Chapter 2 263
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CHAPTER 2 Polynomial and Rational F
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9. (a) (c) 10. (a) (c) y 1 2 x2 (b
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13. f x x 2 5 14. Vertex: Axis of
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25. 27. 29. hx 4x 2 4x 21 Vertex
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41. 2, 2 is the vertex. 42. 2, 0 is
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61. fx 2x 10 2 7x 30 62. x-inter
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75. —CONTINUED— (d) A 8 x50 x
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86. (a) and (c) (b) (d) 1996 (e) Ve
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Section 2.2 Polynomial Functions of
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11. (a) (b) fx x4 fx x 3 3 4 y
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Section 2.2 Polynomial Functions of
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36. (a) 0 with multiplicity 2, 4 an
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49. 51. 53. 55. 57. 59. 61. fx x
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70. 72. 74. gx x 2 10x 16 x 2x
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81. 83. 85. Zeros: 0, 2, 2 all of m
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92. (a) 93. (c) 200 7 140 V 4 3r 3
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111. 113. 115. 117. 12x 2 11x 5
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2x 4 4. and y2 x 3 x (a) and (b
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20. 22. 24. 26. 28. 29. 31. 33. 3 5
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45. fx 4x (a) 1 4 0 13 4 4 4 4 9 3
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58. f x 3x Factors: x 3, x 2 3
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67. 69. 71. ht t 3 2t 2 7t 2 (a
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79. 83. x n 3 ) x 3n 9x 2n 27x n
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1. 4. 7. a 10 b 6 Section 2.4 Comp
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52. 53. 55. 57. 59. 8 16i 2i 3i 4
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74. 4.5x2 3x 12 0; a 4.5, b 3,
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Section 2.5 Zeros of Polynomial Fun
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18. 19. f x 3x 3 19x 2 33x 9 Po
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−24 (c) Real zeros: 2, 1 145 ± 8
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47. 48. fx 2x 3 3x 2 50x 75 Sin
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54. f x x Since 1 3i is a zero, s
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69. 71. 73. gx x 4 4x 3 8x 2 16
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79. Let fx x4 gx 5x 2. 5 10x 5
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99. fx x Rational zeros: 1 x 1 Ir
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111. 9,000,000 0.0001x 2 60x 150,
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129. 3 6i 8 3i 3 6i 8 3i 11
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2 x x 2 7. fx 2 x x 2 Domain:
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27. fx (a) Domain: all real number
Page 77 and 78: 35. gs (a) Domain: all real number
Page 79 and 80: 43. 45. f x 2x2 5x 2 2x 2 x 6
Page 81 and 82: 51. 53. 55. hx (a) Domain: all rea
Page 83 and 84: 60. gx (a) Domain: all real number
Page 85 and 86: 72. (a) x-intercepts: (b) 0 x 3
Page 87 and 88: 80. (a) 81. False. Polynomial funct
Page 89 and 90: 4. 5. 8. 10. 3x2 x2 < 1 4 (a) x 2
Page 91 and 92: 17. 19. 20. x 2 2x 3 < 0 18. x 3
Page 93 and 94: 25. 27. 29. 31. 4x 2 4x 1 ≤ 0 2
Page 95 and 96: 39. −2 −1 0 1 2 3 4 5 x Section
Page 97 and 98: Section 2.7 Nonlinear Inequalities
Page 99 and 100: 59. 61. x x x ≥ 0 x 5x 7 Critic
Page 101 and 102: 73. C 0.0031t 3 0.216t 2 5.54t
Page 103 and 104: Review Exercises for Chapter 2 1. (
Page 105 and 106: 9. 11. 13. hx 4x2 4x 13 10. f x
Page 107 and 108: 21. C 70,000 120x 0.055x The min
Page 109 and 110: 41. fx xx 3 x 2 5x 3 (a) The de
Page 111 and 112: 58. f x 3x (a) 4 3 8 20 16 12 16 1
Page 113 and 114: 77. 79. 4 2 4 2 3i 2 1 i 2
Page 115 and 116: 97. Since is a zero, so is 3x 2x
Page 117 and 118: 111. 114. 117. f x Domain: all rea
Page 119 and 120: 4 126. hx x 1 (a) Domain: all rea
Page 121 and 122: 133. 135. fx 3x3 2x 2 3x 2 3x 2
Page 123 and 124: 142. 144. 146. 148. 12x 3 20x 2 <
Page 125 and 126: 3. V l w h x 2 x 3 x 2 x 3 2
Page 127: Problem Solving for Chapter 2 261 1
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C H A P T E R 2 Polynomial and Rational Functions

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