# How do you find vertical, horizontal and oblique asymptotes for g(x)=5^x?

Sep 5, 2017

There will be a horizontal asymptote at $y = 0$.

#### Explanation:

The domain of any exponential function is $\left\{x | x \in \mathbb{R}\right\}$, so no vertical asymptotes.

As for horizontal asymptotes, the following limit will be determinative:

${\lim}_{x \to - \infty} {5}^{x}$

Calling the limit $L$, we have:

$L = {\lim}_{x \to - \infty} {5}^{x}$

If we think about it, we realize that the closer the number $x = a$ gets to $- \infty$, the closer $L$ will get to $0$. This is because ${a}^{-} n = \frac{1}{a} ^ n$, and $\frac{1}{\infty} = 0$.

So something like ${5}^{-} 1000$ would be very close to $0$. Therefore, we can say that $g \left(x\right)$ has a horizontal asymptote at $y = 0$.

There will be no oblique asymptote for $g \left(x\right)$.

Hopefully this helps!