Stitz-Zeager_College_Algebra_e-book

14 tells us every function we have studied thus far

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Unformatted text preview: cal asymptotes: x = −3, x = 3 As x → −3− , f (x) → ∞ As x → −3+ , f (x) → −∞ As x → 3− , f (x) → −∞ As x → 3+ , f (x) → ∞ No holes in the graph Horizontal asymptote: y = 3 As x → −∞, f (x) → 3+ As x → ∞, f (x) → 3− (j) f (x) = x3 + 2x2 + x x(x + 1) = 2−x−2 x x−2 Domain: (−∞, −1) ∪ (−1, 2) ∪ (2, ∞) x-intercept: (0, 0) y -intercept: (0, 0) Vertical asymptote: x = 2 As x → 2− , f (x) → −∞ As x → 2+ , f (x) → −∞ Hole at (−1, 0) Slant asymptote: y = x + 3 As x → −∞, f (x) → −∞ As x → ∞, f (x) → ∞ y 9 8 7 6 5 4 3 2 1 −9−8−7−6−5−4−3−2−11 − 123456789 −2 −3 −4 −5 −6 −7 −8 −9 y (k) f (x) = 18 16 14 12 10 8 6 4 2 −9 8 7 6 5 4 3 2 1 −−−−−−−− −2 123456789 −4 −6 −8 −10 −x3 + 4x x2 − 9 Domain: (−∞, −3) ∪ (−3, 3) ∪ (3, ∞) x-intercepts: (−2, 0), (0, 0), (2, 0) y -intercept: (0, 0) Vertical asymptotes: x = −3, x = 3 As x → −3− , f (x) → ∞ As x → −3+ , f (x) → −∞ As x → 3− , f (x) → ∞ As x → 3...
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