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

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 $d \left(x\right) = 0$
$\Rightarrow {x}^{2} = 0$
$x = 0$

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

In $n \left(x\right)$, the leading degree is $0$, since ${x}^{0}$ gives $1$. Denote this as $\textcolor{v i o \le t}{n}$.
In $d \left(x\right)$, the leading degree is $2$. Denote this as $\textcolor{g r e e n}{m}$.

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]}