Stitz-Zeager_College_Algebra_e-book

Both ways are demonstrated in the following example

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Unformatted text preview: + , f (x) → −∞ Slant asymptote: y = −x As x → −∞, f (x) → ∞ As x → ∞, f (x) → −∞ (l) f (x) = y 7 6 5 4 3 2 1 −6 −5 −4 −3 −2 −1 −1 −2 −3 −4 −5 −6 −7 1 2 3 4 5 6 x x x 4.2 Graphs of Rational Functions x2 − 2x + 1 x3 + x2 − 2x Domain: (−∞, −2) ∪ (−2, 0) ∪ (0, 1) ∪ (1, ∞) x−1 f (x) = , x=1 x(x + 2) No x-intercepts No y -intercepts Vertical asymptotes: x = −2 and x = 0 As x → −2− , f (x) → −∞ As x → −2+ , f (x) → ∞ As x → 0− , f (x) → ∞ As x → 0+ , f (x) → −∞ Hole in the graph at (1, 0) Horizontal asymptote: y = 0 As x → −∞, f (x) → 0− As x → ∞, f (x) → 0+ 265 (m) f (x) = y 5 4 3 2 1 −5 −4 −3 −2 −1 1 2 3 4 −1 −2 −3 −4 −5 y 1 x−2 1 Shift the graph of y = x to the right 2 units. 4. (a) f (x) = 3 2 1 −1 1 2 3 4 5 x −1 −2 −3 3 x 1 Vertically stretch the graph of y = x by a factor of 3. 3 Reflect the graph of y = x about the x-axis. 3 Shift the graph of y = − x up 1 unit. (b) g...
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