# How do you find the asymptotes for h(x)=(x^2-4) / x?

Mar 30, 2016

vertical asymptote x = 0
oblique asymptote y=x

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation , set the denominator to zero.

hence : x = 0 is the asymptote

Horizontal asymptotes occur when the degree of the numerator is ≤ to the degree of the denominator. This is not so here , hence there are no horizontal asymptotes.

Oblique asymptotes occur when the degree of the numerator > than the degree of the denominator. This is the case here.

divide numerator by x

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

As$x \to \infty , \frac{4}{x} \to 0 \text{ and } y \to x$

$\Rightarrow y = x \text{ is the asymptote }$

Here is the graph of the function.
graph{(x^2-4)/x [-10, 10, -5, 5]}