Question

How do you find the vertical asymptote of an exponential function?

Answer 1

Hint: To solve such a question we should know what the asymptote of a function is. It is simply a straight line that continually approaches a given curve but does not meet it at any finite distance and an exponential function is a Mathematical function in form \[f\text{ }\left( x \right)\text{ }=\text{ }{{a}^{x}}\], where $x$ is a variable and $a$ is a constant .

Complete step by step solution:
For an exponential function, there is no vertical asymptote, as $x$ may have any value.
For the horizontal asymptote, we look at what happens if we let x grow, both positively and negatively.
\[x\to +\infty \]
The function will be greater without limit. No asymptote there.
\[x\to -\infty \]
The function will get smaller and smaller, not ever quite reaching $0$, so \[y=0~\] is an asymptote, or also we can write it as
\[\underset{x\to -\infty }{\mathop{\lim }}\,f(x)=0\]

Note:
The asymptotes of a function are simply a straight line that continually approaches a given curve but does not meet it at any finite distance.
An exponential function is a Mathematical function in form \[f\text{ }\left( x \right)\text{ }=\text{ }{{a}^{x}}\], where $x$ is a variable and $a$ is a constant .