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

May 31, 2018

Domain: $\left\{x | x \ne 0\right\}$ or $\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

Range: $\left\{y | y > 0\right\}$ or $\left(0 , \infty\right)$

#### Explanation:

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

The function is undefined if the denominator is zero, so we set it equal to 0 and solve:

${x}^{2} = 0$

$x = \pm \sqrt{0}$

$x = 0$

So the domain is:

$\left\{x | x \ne 0\right\}$ or $\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

Now as $x$ gets close to $- \infty$ or $\infty$ the function gets closer to 0 but never actually gets to 0 and as $x$ gets very close to 0 the function grows to $\infty$ so the range is:

$\left\{y | y > 0\right\}$ or $\left(0 , \infty\right)$

graph{y = 3/x^2 [-10, 10, -5, 5]}