# What is the domain and range of y= x^2 / (x^2-16) ?

Jul 15, 2017

Domain: $\left(- \infty , - 4\right) \cup \left(- 4 , 4\right) \cup \left(4 , \infty\right)$
Range: $\left(- \infty , \infty\right)$

#### Explanation:

$y = {x}^{2} / \left({x}^{2} - 16\right)$

The denominator cannot be 0, or else the equation would be undefined.

${x}^{2} - 16 \ne 0$
${x}^{2} \ne 16$
$x \ne \pm 4$

$x$ cannot equal $4$ or $- 4$, so the domain is restricted at these values. The range is not restricted; $y$ can take any value.

Domain: $\left(- \infty , - 4\right) \cup \left(- 4 , 4\right) \cup \left(4 , \infty\right)$
Range: $\left(- \infty , \infty\right)$

We can check this by graphing the equation:

graph{x^2/(x^2-16) [-14.24, 14.24, -7.12, 7.12]}