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Stitz-Zeager_College_Algebra_e-book

D j x reect the graph of y about the x axis shift

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Unformatted text preview: ) (very small (+)) 2 (very small (+)) very small (+) We conclude that as x → −2+ , f (x) → ∞. • The behavior of y = f (x) as x → 2: Consider x → 2− . We imagine substituting x = 1.999999. Approximating f (x) as we did above, we get f (x) ≈ 6 3 3 = ≈ ≈ very big (−) (very small (−)) (4) 2 (very small (−)) very small (−) We conclude that as x → 2− , f (x) → −∞. Similarly, as x → 2+ , we imagine substituting 3 x = 2.000001, we get f (x) ≈ very small (+) ≈ very big (+). So as x → 2+ , f (x) → ∞. Graphically, we have that near x = −2 and x = 2 the graph of y = f (x) looks like6 y −3 −1 1 3 x 5. Next, we determine the end behavior of the graph of y = f (x). Since the degree of the numerator is 1, and the degree of the denominator is 2, Theorem 4.2 tells us that y = 0 is the horizontal asymptote. As with the vertical asymptotes, we can glean more detailed 3x information using ‘number sense’. For the discussion below, we use the formula f (x) = x2 −4 . • The be...
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