Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 402: 136

Answer

$f(x)=\frac{x^2-x-2}{x-1}$
1582203174

Work Step by Step

Step 1. With a vertical asymptote of $x=1$; we can write part of the function as $f(x)=\frac{1}{x-1}$ Step 2. With a slant asymptote of $y=x$, we can modify the function as $f(x)=x+\frac{1}{x-1}=\frac{x^2-x}{x-1}$ Step 3. To get a y-intercept at 2, we modify the function as $f(x)=\frac{x^2-x-2}{x-1}$ Step 4. Checking the above function for the x-intercept, we have $x=-1,2$ Step 5. Thus, one possible answer is $f(x)=\frac{x^2-x-2}{x-1}$
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