Stitz-Zeager_College_Algebra_e-book

Our solutions are x 1 and x 0 2 2 to solve the

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Unformatted text preview: havior of y = f (x) as x → −∞: If we were to make a table of values to discuss the behavior of f as x → −∞, we would substitute very ‘large’ negative numbers in for x, say, for example, x = −1 billion. The numerator 3x would then be −3 billion, whereas 5 The actual retail value of f (−2.000001) is approximately −1,500,000. We have deliberately left off the labels on the y -axis because we know only the behavior near x = ±2, not the actual function values. 6 250 Rational Functions the denominator x2 − 4 would be (−1 billion)2 − 4, which is pretty much the same as 1(billion)2 . Hence, f (−1 billion) ≈ −3 billion 3 ≈− ≈ very small (−) 2 1(billion) billion Notice that if we substituted in x = −1 trillion, essentially the same kind of cancellation would happen, and we would be left with an even ‘smaller’ negative number. This not only confirms the fact that as x → −∞, f (x) → 0, it tells us that f (x) → 0− . In other words, the graph of y = f (x) is a little bit below the x-axis...
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