How to find the asymptotes of g(x)=5^x?

May 31, 2016

There is a horizontal asymptote of y=0
No vertical asymptote.

Explanation:

As $x$ becomes increasingly larger as $x > 0$ the ${5}^{x}$ becomes increasingly larger.

So for $x > 0 \text{ } {\lim}_{x \to {\textcolor{w h i t e}{}}^{+} \infty} {5}^{x} = \infty$

So as $x$ is capable of increasing to $\infty$ there is no vertical asymptote for $x > 0$
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For $x < 0$ then ${5}^{x} = \frac{1}{5} ^ x$

As $x$ becomes increasing larger (but negative) then ${5}^{x} = \frac{1}{5} ^ x$ becomes increasingly smaller.

So for $x < 0 \text{ } {\lim}_{x \to {\textcolor{w h i t e}{}}^{-} \infty} {5}^{x} = 0$

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There is a horizontal asymptote of y=0