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

More documents

Recommendations

Info

222 Chapter 2 Polynomial and Rational Functions Section 2.7 Nonlinear Inequalities 1. x2 3 < 0 2. ■ You should be able to solve inequalities. (a) (a) (a) Find the critical number. x 3 3 2 3 < ? 0 6 < 0 No, x 3 is not a solution. x 2 x 12 ≥ 0 x 5 5 2 5 12 ≥ ? 0 Yes, x 5 is a solution. 3. x 2 ≥ 3 x 4 (a) x 5 1. Values that make the expression zero 2. Values that make the expression undefined (b) Test one value in each test interval on the real number line resulting from the critical numbers. (c) Determine the solution intervals. Vocabulary Check 1. critical; test intervals 2. zeros; undefined values 3. P R C 5 2 5 4 ≥? 3 7 ≥ 3 Yes, x 5 is a solution. 8 ≥ 0 (b) (b) x 0 (c) 0 2 3 < ? 0 3 < 0 Yes, x 0 is a solution. x 0 (c) 0 2 0 12 ≥ ? 0 12 ≥ 0 No, x 0 is not a solution. (b) 4 2 4 4 6 is undefined. 0 No, x 4 is not a solution. ≥? x 4 3 (c) x 3 2 3 2 2 3 < ? 0 3 4 < 0 Yes, x is a solution. 3 2 4 2 4 12 ≥ ? 0 16 4 12 ≥ ? 0 8 ≥ 0 Yes, x 4 is a solution. (d) x 4 (d) x 9 2 92 2 9 2 4 ≥? 3 5 ≥ 3 17 No, x is not a solution. 9 2 (d) x 5 5 2 3 < ? 0 22 < 0 No, x 5 is not a solution. x 3 3 2 3 12 ≥ ? 0 9 3 12 ≥ ? 0 0 ≥ 0 Yes, x 3 is a solution. x 9 2 9 2 2 9 2 4 ≥? 3 13 ≥ 3 Yes, x is a solution. 9 2
4. 5. 8. 10. 3x2 x2 < 1 4 (a) x 2 322 2 2 4
Page 1 and 2:
CHAPTER 2 Polynomial and Rational F
Page 3 and 4:
9. (a) (c) 10. (a) (c) y 1 2 x2 (b
Page 5 and 6:
13. f x x 2 5 14. Vertex: Axis of
Page 7 and 8:
25. 27. 29. hx 4x 2 4x 21 Vertex
Page 9 and 10:
41. 2, 2 is the vertex. 42. 2, 0 is
Page 11 and 12:
61. fx 2x 10 2 7x 30 62. x-inter
Page 13 and 14:
75. —CONTINUED— (d) A 8 x50 x
Page 15 and 16:
86. (a) and (c) (b) (d) 1996 (e) Ve
Page 17 and 18:
Section 2.2 Polynomial Functions of
Page 19 and 20:
11. (a) (b) fx x4 fx x 3 3 4 y
Page 21 and 22:
Section 2.2 Polynomial Functions of
Page 23 and 24:
36. (a) 0 with multiplicity 2, 4 an
Page 25 and 26:
49. 51. 53. 55. 57. 59. 61. fx x
Page 27 and 28:
70. 72. 74. gx x 2 10x 16 x 2x
Page 29 and 30:
81. 83. 85. Zeros: 0, 2, 2 all of m
Page 31 and 32:
92. (a) 93. (c) 200 7 140 V 4 3r 3
Page 33 and 34:
111. 113. 115. 117. 12x 2 11x 5
Page 35 and 36:
2x 4 4. and y2 x 3 x (a) and (b
Page 37 and 38: 20. 22. 24. 26. 28. 29. 31. 33. 3 5
Page 39 and 40: 45. fx 4x (a) 1 4 0 13 4 4 4 4 9 3
Page 41 and 42: 58. f x 3x Factors: x 3, x 2 3
Page 43 and 44: 67. 69. 71. ht t 3 2t 2 7t 2 (a
Page 45 and 46: 79. 83. x n 3 ) x 3n 9x 2n 27x n
Page 47 and 48: 1. 4. 7. a 10 b 6 Section 2.4 Comp
Page 49 and 50: 52. 53. 55. 57. 59. 8 16i 2i 3i 4
Page 51 and 52: 74. 4.5x2 3x 12 0; a 4.5, b 3,
Page 53 and 54: Section 2.5 Zeros of Polynomial Fun
Page 55 and 56: 18. 19. f x 3x 3 19x 2 33x 9 Po
Page 57 and 58: −24 (c) Real zeros: 2, 1 145 ± 8
Page 59 and 60: 47. 48. fx 2x 3 3x 2 50x 75 Sin
Page 61 and 62: 54. f x x Since 1 3i is a zero, s
Page 63 and 64: 69. 71. 73. gx x 4 4x 3 8x 2 16
Page 65 and 66: 79. Let fx x4 gx 5x 2. 5 10x 5
Page 67 and 68: 99. fx x Rational zeros: 1 x 1 Ir
Page 69 and 70: 111. 9,000,000 0.0001x 2 60x 150,
Page 71 and 72: 129. 3 6i 8 3i 3 6i 8 3i 11
Page 73 and 74: 2 x x 2 7. fx 2 x x 2 Domain:
Page 75 and 76: 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: 80. (a) 81. False. Polynomial funct
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 and 128: Problem Solving for Chapter 2 261 1
Page 129: 19. Use synthetic division to show
show all

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

Create successful ePaper yourself

Delete template?

Save as template?