How do you find vertical, horizontal and oblique asymptotes for #F(x)= (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.

#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 # y = x^2/x - 4/x = x - 4/x#

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]}