Question

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

Answer 1

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]}