# How do I find the asymptotes of y=-1/x^2?

Sep 13, 2015

Horizontal asymptote at: $y = 0$

Vertical asymptote at: $x = 0$

#### Explanation:

$y = - \frac{1}{x} ^ 2$

The horizontal asymptote is at : lim(x to +-oo) $\left(y\right)$

So in this case:

lim(x to +-oo) $\left(- \frac{1}{x} ^ 2\right) \implies$

as x tends to infinity the denominator keeps getting larger and

larger forcing the fraction to tend to zero, hence: the horizontal

asymptote is at $y = 0$, AKA the x-axis

The vertical asymptote(s) are the at the value(s) of x that make the

function $f \left(x\right) = y$ undefined hence the vertical asymptote in this

case is at:

$x = 0$, AKA the y-axis.