# How do you find the asymptote of an exponential function?

Feb 19, 2016

There is no vertical asymptote, as $x$ may have any value.

#### Explanation:

For the horizontal asymptote we look at what happens if we let $x$ grow, both positively and negatively.

$x \to + \infty$
The function will be greater without limit. No asymptote there.

$x \to - \infty$
The function will get smaller and smaller, not ever quite reaching $0$, so $y = 0$ is an asymptote, or in 'the language':

${\lim}_{x \to - \infty} f \left(x\right) = 0$
graph{0.1*e^x [-30.37, 20.96, -12.52, 13.15]}