# How do you find the Vertical, Horizontal, and Oblique Asymptote given f(x) = 4/(x - 2)^3?

Nov 10, 2016

The vertical asymptote is $x = 2$
The horizontal asymptote is $y = 0$
There are no oblique asymptote.

#### Explanation:

As we cannot divide by $0$, the vertical asymptote is $x = 2$

There are no oblique asymptotes as the degree of the numerator is $<$ degree of the denominator:

${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to - \infty} \left(\frac{4}{x} ^ 3\right) = {0}^{-}$

${\lim}_{x \to + \infty} f \left(x\right) = {\lim}_{x \to + \infty} \left(\frac{4}{x} ^ 3\right) = {0}^{+}$

The horizontal asymptote is $y = 0$

graph{4/(x-2)^3 [-10, 10, -5, 5]}