# Can a function have a vertical asymptote?

May 16, 2018

Yes.

#### Explanation:

A function can have a vertical asymptote,

One such function is $\frac{a}{x}$, where $a$ is a constant.

When $a = 1$,

graph{1/x [-10, 10, -5, 5]}

When $a = - 1$,

graph{-1/x [-10, 10, -5, 5]}

In both cases, the graph does not intersect the y-axis, which is a vertical line, making the y-axis an asymptote of $\frac{a}{x}$.