# How do you find vertical and horizontal asymptotes of (4x)/(x-3)?

Aug 19, 2015

There is a vertical asymptote at $\textcolor{red}{x = 3}$ and a horizontal asymptote at $\textcolor{red}{y = 4}$.

#### Explanation:

$f \left(x\right) = \frac{4 x}{x - 3}$

Step 1. Find the vertical asymptotes.

Set the denominator equal to zero and solve for $x$.

$x - 3 = 0$

$x = 3$

There is a vertical asymptote at $x = 3$.

Step 3. Find the horizontal asymptotes.

Since the numerator and denominator are the same degree, we must divide the coefficients of the highest terms.

$\frac{4}{1} = 4$

The horizontal asymptote is at $y = 4$.