Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Test - Page 434: 23


domain: $(-\infty,2)\cup(2,\infty)$ See graph.

Work Step by Step

Step 1. Factor the function as $f(x)=\frac{(x+3)(x-3)}{x-2}$; there are no common factors. Step 2. The domain requirement is that the denominator can not be zero, which gives $x\ne2$. Thus the domain can be written as $(-\infty,2)\cup(2,\infty)$ Step 3. Rewrite the function as $f(x)=\frac{x^2-4-5}{x-2}=x+2-\frac{5}{x-2}$; we can find a slant asymptote as $y=x+2$ Step 4. See graph.
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