Stitz-Zeager_College_Algebra_e-book

278 433 rational functions answers 6 1 a x 7 b

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Unformatted text preview: of the graph of g and any holes in the graph, if they exist. Be sure to show all of your work including any polynomial or synthetic division. Sketch the graph of g , using more than one picture if necessary to show all of the important features of the graph. 6. Let g (x) = 4.2 Graphs of Rational Functions 4.2.2 261 Answers 1. (a) y = x 2 (b) y = 3 x + (c) y = −5x − 18 11 9 4 x+2 Domain: (−∞, −2) ∪ (−2, ∞) No x-intercepts y -intercept: (0, 2) Vertical asymptote: x = −2 As x → −2− , f (x) → −∞ As x → −2+ , f (x) → ∞ Horizontal asymptote: y = 0 As x → −∞, f (x) → 0− As x → ∞, f (x) → 0+ (d) y = −x 2. (a) f (x) = 5x 6 − 2x Domain: (−∞, 3) ∪ (3, ∞) x-intercept: (0, 0) y -intercept: (0, 0) Vertical asymptote: x = 3 As x → 3− , f (x) → ∞ As x → 3+ , f (x) → −∞ 5 Horizontal asymptote: y = − 2 + As x → −∞, f (x) → − 5 2 − As x → ∞, f (x) → − 5 2 y 5 4 3 2 1 2 3 4 5 x 5 6 7 8 9 x −2 −3 −4...
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