How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)= 1/x^2#?

1 Answer
Oct 14, 2017

Answer:

Vertical asymptote: #x=0#
Horizontal asymptote: #y=0#

Explanation:

Denote the function as #(n(x))/(d(x)#

To find the vertical asymptote,
Solve #d(x)=0#
#rArr x^2=0#
#x=0#

To find the horizontal asymptote,
Compare the leading degrees of the numerator and the denominator.

In #n(x)#, the leading degree is #0#, since #x^0# gives #1#. Denote this as #color(violet)n#.
In #d(x)#, the leading degree is #2#. Denote this as #color(green)m#.

When #n < m#, the #x#- axis (that is #y=0#) is the horizontal asymptote.

graph{1/x^2 [-10.04, 9.96, -0.36, 9.64]}