# How to find the asymptotes of h(x)=5^(x-2)?

Feb 22, 2018

Take the limits of $h \left(x\right)$ as x->+-∞ to determine the horizontal asymptotes.

#### Explanation:

Take the limits of $h \left(x\right)$ as x->+-∞ to determine the function's horizontal asymptotes. We have no vertical asymptotes, as there are no values of $x$ that will make this function undefined.

Lim_(x->∞)5^(x-2)=5^∞=∞ (No asymptotes as we approach +∞.

Lim_(x->-∞)5^(x-2)=5^-∞=1/5^∞=0

So, $y = 0$ is this function's only horizontal asymptote, as we approach $y = 0$ for smaller and smaller values of $x$ but never cross/touch it.