Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - True-False Quiz - Page 166: 15

Answer

The statement is false.

Work Step by Step

When a function contains a vertical asymptote at $x=1$ (see the image for an example), we know that $y=f(1)$ is undefined at $x=1$. However, a piecewise function can nevertheless be defined at $x=1$, while containing an asymptote there. For example, consider the piecewise function: $f(x)=\frac{2}{x-1}$ for $x\ne 1$ $f(x)=5$ for $x=1$ Such a function would contain an asymptote at $x=1$, while still being defined at $x=1$ -- that is, $f(1)=5$. Thus, the statement is false.
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