# How do you find the vertical, horizontal or slant asymptotes for 2 - 3/x^2?

Nov 28, 2016

The vertical asymptote is $x = 0$
No slant asymptote
The horizontal asymptote is $y = 2$

#### Explanation:

Let $f \left(x\right) = 2 - \frac{3}{x} ^ 2$

The domain of $f \left(x\right)$ is $\mathbb{R} - \left\{0\right\}$

As you cannot divide by $0$, $x \ne 0$

So, the vertical asymptote is $x = 0$

As the degree of the numerator is $=$ th the degree of the denominator, there is no slant asymptote.

${\lim}_{x \to \pm \infty} f \left(x\right) = i {m}_{x \to \pm \infty} \left(2 - \frac{3}{x} ^ 2\right) = 2$

The horizontal asymptote is $y = 2$

graph{(y-(2-3/x^2))(y-2)=0 [-7.9, 7.9, -3.95, 3.95]}