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

Nov 11, 2015

$y = 0$

#### Explanation:

For any function f(x), horizontal asymptotes occur at ${\lim}_{x \to \pm \infty} f \left(x\right)$.

In this case, ${\lim}_{x \to - \infty} {5}^{x} = 0 \mathmr{and} {\lim}_{x \to \infty} {5}^{x} = \infty$.

hence there is a horizontal asymptote at $y = 0$.

This is clear from the graph of the function given below :

graph{5^x [-16.79, 11.69, -4.84, 9.4]}