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

Mar 26, 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, let the denominator equal zero.

hence : x = 0 is the asymptote

Horizontal asymptotes occur as lim_(x→±∞) f(x) → 0

When the degree of the numerator is greater than the degree of the denominator, there will be no horizontal asymptotes , but there will be an oblique asymptote.

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

As x→±∞ ,  4/x → 0 " and " y → x#

$\Rightarrow y = x \text{ is an oblique asymptote }$
graph{(x^2-4)/x [-10, 10, -5, 5]}