Vertical Asymptotes

**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:

\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:**