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

##### 1 Answer

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.

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

# (x^2-4)/x = x^2/x - 4/x = x - 4/x # As x→±∞ ,

# 4/x → 0 " and " y → x#

# rArr y = x " is an oblique asymptote " #

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