Vertical Asymptote: When simplified, vertical asymptotes are x-values that make the denominator zero.

Example 1: (1)
\begin{align} f(x)=\frac{1}{x}\ \end{align}

Both x and y are asymptotes of the function.
As you can see in Ex 1, the function gets close to the axis but will ever touch either of them. An asymptote is a number that the function can not be.

To Find:
-Set the denominator to equal zero and solve for the vertical asymptote.

Example 2:
Find the vertical asymptote:

(2)
\begin{align} f(x)=\frac{3x-1}{x+5}\ \end{align}
Step 1:
Set the denominator equal to zero
x+5=0
Step 2:
Solve for x
x+5=0
x=-5
Answer: There is a vertical asymptote at x=-5.
Graphing: Make a line going vertically through the point found (x=-5)
Example: