# How do you find vertical, horizontal and oblique asymptotes for f(x)=(3x)/(x-8)?

Oct 30, 2016

The vertical asymptote is $x = 8$
The horizontal asymptote is $y = 3$
There is no oblique asymptote

#### Explanation:

As you cannot divide by $0$, so $x \ne 8$
Therefore the vertical asymptote is $x = 8$

As the degree of the numerator is equal to the degree of the denominator, there is no oblique asymptote.

Limit $f \left(x\right) = \frac{3 x}{x} = 3$
$x \to \pm \infty$
Therefore $y = 3$ is a horizontal asymptote

graph{3x/(x-8) [-65.8, 65.9, -32.9, 33]}