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: 127


The given statement does not make sense. The graph has a vertical asymptote only at $x=2$

Work Step by Step

The given function is $f\left( x \right)=\frac{x-1}{\left( x-1 \right)\left( x-2 \right)}$. Simplifying the above function as, $\begin{align} & f\left( x \right)=\frac{x-1}{\left( x-1 \right)\left( x-2 \right)} \\ & =\frac{1}{\left( x-2 \right)} \end{align}$ Now, the vertical asymptotes is determined by equating the denominator to 0; thus, we’ll get $\begin{align} & x-2=0 \\ & x=2 \end{align}$ Therefore, the vertical asymptote is $x=2$ and there is no vertical asymptote at $x=1$. Thus, the given statement does not make sense.
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