# What are the asymptotes for h(x)=5^(x-2)?

Aug 7, 2015

The only asymptote is the $x$-axis: $\textcolor{red}{h \left(x\right) = 0}$

#### Explanation:

The domain consists of all real numbers.

The range consists of all real numbers from zero to infinity, because ${5}^{x - 2}$ is always positive.

As $x$ becomes increasingly negative, $h \left(x\right)$ gets increasingly closer to zero.

The $x$ axis or $h \left(x\right) = 0$ is the horizontal asymptote.