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Stitz-Zeager_College_Algebra_e-book

# A 3 a f x 3x2 4 f 1 x log3 x 4 2 b

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Unformatted text preview: main: (−∞, −2) ∪ (−2, ∞) (+) (−) 0 (+) (d) f (x) = √ 3 8 7 6 5 4 3 2 1 −2 0 Vertical asymptote x = −2 Horizontal asymptote y = 5 No unusual steepness or cusps Using Calculus it can be shown that y = x − 1 y 1 (c) f (x) = x 3 (x − 7) 3 Domain: (−∞, ∞) (−) 0 (−) 0 (+) 12 2 −4 −3 −2 −1 1 − −2 −3 −4 −5 −6 7 3 is a slant asymptote of this graph. 7 8 9 x 7 8 x 5.3 Other Algebraic Functions 3 325 y 1 (e) f (x) = x 2 (x − 7) 3 Domain: [0, ∞) (−) 0 0 (+) 0 7 No asymptotes Unusual steepness at x = 7 No cusps 25 20 15 10 5 1 2 3 4 5 6 7 −5 8x −10 −15 y (f) f (x) = x(x + 5)(x − 4) Domain: [−5, 0] ∪ [4, ∞) 0 (+) 0 0 (+) 9 8 7 6 −5 0 4 No asymptotes Unusual steepness at x = −5, x = 0 and x=4 No cusps 5 4 3 2 1 1 √ (g) f (x) = 3 x3 + 3x2 − 6x − 8 Domain: (−∞, ∞) (−) 0 (+) 0 (−) 0 (+) 2 3 4 5 x 1 −5 −4 −3 −2 −1 2 3 4 5 x y 6 5 4 3 −4 −1 2 No vertical or horizontal asymptotes13 Unusual steepness at x =...
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