How many vertical asymptotes can a graph have?

Sep 2, 2014

A graph can have an infinite number of vertical asymptotes.

For example,

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

has n vertical asymptotes; namely,

$x = 1$, $x = 2$, $x = 3$, and $x = n$.

(Remark: A graph has at most two horizontal asymptotes.)