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

##### 1 Answer

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.

#rArr x = 0 " 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

As x → ±∞ ,

# 4/x → 0 and y → x#

# rArr y = x " is the asymptote " # Here is the graph of the function.

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