Stitz-Zeager_College_Algebra_e-book

# Being quotients of polynomials we can ultimately view

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Unformatted text preview: (−2, 2) ∪ (2, ∞) x-intercept: (0, 0) y -intercept: (0, 0) Vertical asymptotes: x = −2, x = 2 As x → −2− , f (x) → −∞ As x → −2+ , f (x) → ∞ As x → 2− , f (x) → −∞ As x → 2+ , f (x) → ∞ No holes in the graph Horizontal asymptote: y = 0 As x → −∞, f (x) → 0− As x → ∞, f (x) → 0+ y 1 −7 −6 −5 −4 −3 −2 −1 2 3 4 5 6 7 x −1 y (h) f (x) = x2 − x − 12 x−4 = 2+x−6 x x−2 Domain: (−∞, −3) ∪ (−3, 2) ∪ (2, ∞) x-intercept: (4, 0) y -intercept: (0, 2) Vertical asymptote: x = 2 As x → 2− , f (x) → ∞ As x → 2+ , f (x) → −∞ 7 Hole at −3, 5 Horizontal asymptote: y = 1 As x → −∞, f (x) → 1+ As x → ∞, f (x) → 1− 1 5 4 3 2 1 −5 −4 −3 −2 −1 1 2 3 4 5 x 1 2 3 4 5 x −1 −2 −3 −4 −5 y (i) f (x) = 5 4 3 2 1 −5 −4 −3 −2 −1 −1 −2 −3 −4 −5 264 Rational Functions (3x + 1)(x − 2) 3x2 − 5x − 2 = 2−9 x (x + 3)(x − 3) Domain: (−∞, −3) ∪ (−3, 3) ∪ (3, ∞) 1 x-intercepts: − 3 , 0 , (2, 0) 2 y -intercept: 0, 9 Verti...
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