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

1 Answer
Oct 14, 2017

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]}