## Calculus 8th Edition

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.