# How do you find vertical, horizontal and oblique asymptotes for F(x)= (x^2-4) / x?

Mar 26, 2016

#### Answer:

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 let the denominator equal zero.

$\Rightarrow x = 0 \text{ is the asymptote }$

There are no horizontal asymptotes , since degree of numerator is greater than degree of numerator. However , this does mean that there is an oblique asymptote.

divide all terms on numerator by x

hence $y = {x}^{2} / x - \frac{4}{x} = x - \frac{4}{x}$

As x → ±∞ ,  4/x → 0 and y → x

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

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