Asymptote VS undefined point When searching for asymptote how do I recognize that it is an undefined point rather than asymptote? the one-sided limits at the asymptote should be $+-\infty$ and when is an undefined point the limits are finite?

By definition:

> a function $y=f(x)$ has a vertical asymptote $x=a$ iff at least one of the limits:
>
> $$ \lim_{x \to a^-}f(x) \qquad \lim_{x \to a^+}f(x) $$
>
> is $\pm \infty$.

As an example, the function: $$ y=\begin{cases} x \quad for \quad x\le0\\\ 1/x \quad for \quad x>0 \end{cases} $$ has the vertical asymptote $x=0$

Note that in this case the function is defined for $x=0$.