# How do you find the asymptotes for y= 2^x?

Feb 24, 2016

There will be no vertical asymptote, because $x$ may have any value.

#### Explanation:

For the horizontal asymptote we look at what happens if $x$ gets larger and larger, both positive and negative:

$x \to + \infty$ then $y \to + \infty$ means no asymptote

$x \to - \infty$ then $y \to 0$ so $y = 0$ is an asymptote

e.g. $x = - 10 \to y = \frac{1}{1024}$ and $x = - 20 \to y = \frac{1}{1048576}$
graph{2^x [-16.02, 16.01, -8.01, 8.01]}