308 CHAPTER 5 Exponential and Logarithmic Functions 35. x f x( ) −1 54 0 18 1 6 2 2 3 2 3 36. x g x( ) −1 6 0 1 1 0 2 3 3 10 37. x H x( ) −1 2 0 4 1 6 2 8 3 10 38. x F x( ) −1 1 2 0 1 4 1 1 8 2 1 16 3 1 32 39. x y 2 22 y 5 0 3 21 40. x y 2 3 21 22 y 5 0 41. y 2 1 23 22 y 5 0 x 42. x y 2 1 23 22 y 5 1 43. x y 2 3 21 22 y 5 0 44. x y 2 1 23 22 y 5 0 45. x y 2 3 21 22 y 5 21 46. x y 2 3 21 22 y 5 0 (A) = y 3x (B) = − y 3 x (C) = − y 3x (D) = − − y 3 x In Problems 39–46, the graph of an exponential function is given. Match each graph to one of the following functions. (E) = − y 3 1 x (F) = − y 3x 1 (G) = − y 3 x 1 (H) = − y 1 3x In Problems 47–58, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. 47. ( ) = + f x 2 1 x 48. ( ) = − f x 3 2 x 49. ( ) = − f x 3x 1 50. ( ) = + f x 2x 2 51. ( ) ( ) = ⋅ f x 3 1 2 x 52. ( ) ( ) = ⋅ f x 4 1 3 x 53. ( ) = − − f x 3 2 x 54. ( ) = − + f x 3 1 x 55. ( ) = + − f x 2 4x 1 56. ( ) = − + f x 1 2x 3 57. ( ) = + f x 2 3x 2 58. ( ) = − − f x 1 2 x/3 In Problems 59–66, begin with the graph of = y ex (Figure 30) and use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. 59. ( ) = − f x e x 60. ( ) = − f x ex 61. ( ) = + f x ex 2 62. ( ) = − f x e 1 x 63. ( ) = − − f x e 5 x 64. ( ) = − − f x e 9 3 x 65. ( ) = − − f x e 2 x 2 66. ( ) = − f x e 7 3 x2 In Problems 67–86, solve each equation. 67. = 6 6 x 5 68. = − 5 5 x 6 69. = −2 16 x 70. = −3 81 x 71. ( ) = 1 5 1 25 x 72. ( ) = 1 4 1 64 x 73. = − 3 9 x2 5 74. = + 5 1 5 x 3 75. = 3 9 x x 3 76. = 4 2 x x 2 77. = − + 8 16 x x 11 2 78. = − + 9 27 x x 15 79. = − 3 27 x x 7 2 2 80. = + 5 125 x x 8 2 2 81. ⋅ = 4 2 16 x x 2 2 82. ⋅ = − 9 27 3 x x 2 1 2 83. = + e e x x 2 5 12 84. = − e e x x 3 2 85. = ⋅ e e e 1 x x3 2 2 86. ( ) ⋅ = e e e x x 4 12 2
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