# How to find the asymptotes of f(x) = 6^(x-2)?

Jan 14, 2016

$y = 0$

#### Explanation:

Find the limit in either infinite direction.

${\lim}_{x \rightarrow \infty} {6}^{x - 2} = {6}^{\infty} = \infty$

${\lim}_{x \rightarrow - \infty} {6}^{x - 2} = {6}^{-} \infty = \frac{1}{6} ^ \infty = 0$

Note that this is just a mental process to undergo.

Thus the asymptote is $y = 0$ (as xrarr-oo).

We can check a graph:

graph{6^(x-2) [-8.535, 13.965, -2.52, 8.73]}