377 3.5 Rational Functions: Graphs, Applications, and Models Graph each rational function. See Examples 5-9 x- 5 X t1 62. f(x) 61. f(x) 1 0 x +3 x- 4 x- 3 64. f(x) 63. f(x) 11 x +4 x- 3 6-3x 4 - 2x 66. f(x) 65. f(x) 11 4-x 8-x 2x 1 3x 67. f(x) 68. f(x) 1 x2 6x+ 8 x2-x- 2 Ce 5x 70. f(x) 69. f(x) = 11 4 x2 x2- 1 (x + 6) (x- 2) (x + 3)(x- 4) (x+3)(x-5) 72. f(x) 71. f(x)= (x+ 1)(x - 4) 3x2 3x- 6 4x24x 24 74. f(x) 73. f(x) x2-x - 12 x2 3x 10 baii doout sl dsg 1os 16x2 9 76. f(x)= 75. f(x) 8-3 ees esirs is osiho x2-9 x2 - 4 IiCLCCbr (o' (x-3) (x + 1) x(x- 2) Aupc Pwwnbre vs lemoso77. f(x) = 78. f(x) 11 (x 1) (x+3)2 inoit -5 80. f(x) = X 79. f(x) x2 - 9 2x 4 8 uiooox .I 0IT (x-5)(x- 2) 1 81. f(x) = 82. f(x) 11 x29 x21 (x+ 1)2 (x + 2)(x-3) olo (x+ 4)2 84. f(x) 83. f(x) 11 11 (x- 1)(x +5) 18 +6x-4x2 20+6x-2x2 86. f(x) 85. f(x) 4+6x+ 2x2 8+6x-2x2
377 3.5 Rational Functions: Graphs, Applications, and Models Graph each rational function. See Examples 5-9 x- 5 X t1 62. f(x) 61. f(x) 1 0 x +3 x- 4 x- 3 64. f(x) 63. f(x) 11 x +4 x- 3 6-3x 4 - 2x 66. f(x) 65. f(x) 11 4-x 8-x 2x 1 3x 67. f(x) 68. f(x) 1 x2 6x+ 8 x2-x- 2 Ce 5x 70. f(x) 69. f(x) = 11 4 x2 x2- 1 (x + 6) (x- 2) (x + 3)(x- 4) (x+3)(x-5) 72. f(x) 71. f(x)= (x+ 1)(x - 4) 3x2 3x- 6 4x24x 24 74. f(x) 73. f(x) x2-x - 12 x2 3x 10 baii doout sl dsg 1os 16x2 9 76. f(x)= 75. f(x) 8-3 ees esirs is osiho x2-9 x2 - 4 IiCLCCbr (o' (x-3) (x + 1) x(x- 2) Aupc Pwwnbre vs lemoso77. f(x) = 78. f(x) 11 (x 1) (x+3)2 inoit -5 80. f(x) = X 79. f(x) x2 - 9 2x 4 8 uiooox .I 0IT (x-5)(x- 2) 1 81. f(x) = 82. f(x) 11 x29 x21 (x+ 1)2 (x + 2)(x-3) olo (x+ 4)2 84. f(x) 83. f(x) 11 11 (x- 1)(x +5) 18 +6x-4x2 20+6x-2x2 86. f(x) 85. f(x) 4+6x+ 2x2 8+6x-2x2
Chapter4: Rational Functions And Conics
Section4.1: Rational Functions And Asymptotes
Problem 50E: The graph of a rational function f(x)=N(x)D(x)is shown below. Determine which of the statements...
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