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

May 1, 2016

One vertical asymptote $x = 0$ and one oblique asymptote $y = x$

#### Explanation:

In $h \left(x\right) = \frac{{x}^{2} - 4}{x}$,

vertical asymptotes are obtained by putting denominator equal to zero.

Hence $x = 0$ is the only vertical asymptote.

As the highest degree of numerator is ${x}^{2}$ and of denominator $x$ are not equal, there is no horizontal asymptote. But it is just one degree higher than that of denominator,

hence we have one oblique asymptote given by $y = {x}^{2} / x = x$

graph{(x^2-4)/x [-16, 16, -8, 8]}