# How do you find the horizontal asymptote for h(x)=5^(x-2)?

Feb 4, 2016

Horizontal asymptote: $h \left(x\right) = 0$
As $x \rightarrow - \infty$
$\textcolor{w h i t e}{\text{XXX}} {\lim}_{x \rightarrow - \infty} {5}^{x - 2}$
$\textcolor{w h i t e}{\text{XXX}} = {\lim}_{x \rightarrow - \infty} \frac{1}{{5}^{\left\mid x - 2 \right\mid}}$
$\textcolor{w h i t e}{\text{XXX}} = 0$