# Do asymptotes always converge to a value?

Mar 25, 2017

No. The function is undefined at the asymptote value.

#### Explanation:

Asymptotes go from $\left(- \infty , \infty\right)$

When a function has a vertical asymptote at a $x - v a l u e$ the function never reaches that value.

Ex. $y = \frac{1}{x - 5}$

The vertical asymptote is at $x = 5$ At $x = 5$ the function is undefined. See the graph below:

graph{1/(x-5) [-5.41, 14.59, -6.04, 3.96]}