# How do you find the asymptotes for e^x / x?

Feb 18, 2018

At $x = 0$ and $y = 0$

#### Explanation:

Vertical asymptotes:

Vertical asymptotes are found when the function is not defined. Here, the denominator must be $0$ for this to occur.

So when $x = 0$, there is an asymptote.

Horizontal asymptotes:

Horizontal asymptotes correspond to the range of a function. $y$ is defined for all values of $x$. However, for any value of $x$, $y$ can never be $0$.

This is because for so, ${e}^{x} = 0$ for a certain value of $x$. However, as this is not possible, there exists an asymptote at $y = 0$.