396 CHAPTER 3 Polynomial and Rational Functions 50. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x = 2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). (a) ƒ1x2 = 1 1x - 222 (b) ƒ1x2 = 1 x - 2 (c) ƒ1x2 = -1 x - 2 (d) ƒ1x2 = -1 1x - 222 Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ1x2. State the domain of ƒ. 53. –10 –6 –2 6 10 –8 –4 6 10 0 x y 54. –10 –6 6 0 8 10 –6 6 10 x y 55. –8 –4 4 0 8 –6 –2 x y 56. –8 4 0 8 –8 –4 8 x y 57. 1 –3 0 1 2 3 x y 58. –3 3 1 0 3 x y 59. x 1 3 –3 0 1 y –1 –4 3 60. x 1 3 –3 0 1 3 5 y –2 –4 –6 A. x 2 B. x 2 C. x 2 D. x 2 51. Which function has a graph that does not have a vertical asymptote? A. ƒ1x2 = 1 x2 + 2 B. ƒ1x2 = 1 x2 - 2 C. ƒ1x2 = 3 x2 D. ƒ1x2 = 2x + 1 x - 8 52. Which function has a graph that does not have a horizontal asymptote? A. ƒ1x2 = 2x - 7 x + 3 B. ƒ1x2 = 3x x2 - 9 C. ƒ1x2 = x2 - 9 x + 3 D. ƒ1x2 = x + 5 1x + 221x - 32
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