Stitz-Zeager_College_Algebra_e-book

Another way to interpret our answer is that innitely

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Unformatted text preview: the graph of g by taking the ratio of the leading terms coefficients, y = 2 = 2. However, if we take the time to do a 1 more detailed analysis, we will be able to reveal some ‘hidden’ behavior which would be lost otherwise.10 As in the discussion following Theorem 4.2, we use the result of the long division 2 2x2 − 3x − 5 ÷ x2 − x − 6 to rewrite g (x) = 2x2 −3x−5 as g (x) = 2 − x2x−7 6 . We focus our x −x−6 −x− attention on the term x2x−7 6 . − x− 10 That is, if you use a calculator to graph. Once again, Calculus is the ultimate graphing power tool. 4.2 Graphs of Rational Functions 253 • The behavior of y = g (x) as x → −∞: If imagine substituting x = −1 billion into x−7 , we estimate x2x−7 6 ≈ −1 billion ≈ very small (−).11 Hence, x2 −x−6 −x− 1billion2 g (x) = 2 − x2 x−7 ≈ 2 − very small (−) = 2 + very small (+) −x−6 In other words, as x → −∞, the graph of y = g (x) is a little bit above the line y = 2. • The behavior of y = g (x) as x → ∞. To consider...
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