# How do you find the domain and range of y = 3/x^2?

Apr 26, 2017

Domain: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$
Range: $\left(0 , + \infty\right)$

#### Explanation:

$y = \frac{3}{x} ^ 2$

$y$ is defined $\forall x \in \mathbb{R} : x \ne 0$

Hence the domain of $y$ is $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

Consider both:

${\lim}_{\text{x->+-0}} \frac{3}{x} ^ 2 = \infty$

and
${\lim}_{\text{x->+-oo}} \frac{3}{x} ^ 2 = 0$

Hence the range of $y$ is $\left(0 , + \infty\right)$

These can be seen from the graph of $y$ below:

graph{3/x^2 [-6.967, 7.08, -0.73, 6.294]}