Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - Review - True-False Quiz: 19

Answer

False.

Work Step by Step

A function can be defined piecewise. For example, $f(x)=\left\{\begin{array}{ll} \dfrac{1}{x-1}, & x\neq 1\\ 0, & x=1 \end{array}\right.$ By definition of vertical asymptote (see p.58), $\displaystyle \lim_{x\rightarrow 1^{+}}f(x)=\infty$, f is a function with a vertical asymptote x=1, but f(1) IS defined.
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