# What does vertical asymptote mean?

Sep 25, 2014

A vertical line $x = a$ is called a vertical asymptote of a function $f \left(x\right)$ if one of the following is true:

${\lim}_{x \to {a}^{-}} f \left(x\right) = \pm \infty$, or ${\lim}_{x \to {a}^{+}} f \left(x\right) = \pm \infty$.

Let us look at the vertical asymptotes of

$f \left(x\right) = \frac{1}{\left(x + 2\right) \left(x - 3\right)}$.

As we can see in the graph above,

${\lim}_{x \to - {2}^{-}} f \left(x\right) = + \infty$,

makes $x = - 2$ (in red) a vertical asymptote, and

${\lim}_{x \to {3}^{-}} f \left(x\right) = - \infty$,

makes $x = 3$ (in blue) a vertical aymptote.