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.
