# What is the domain and range of y=x^2-9?

Apr 25, 2018

Assuming we are limited to Real numbers:
Domain: $x \in \mathbb{R}$
Range: $y \in \left[- 9 , + \infty\right)$

#### Explanation:

$y = {x}^{2} - 9$ is defined for all Real values of $x$ (actually it is defined for all Complex values of $x$ but let's not worry about that).

If we are restricted to Real values, then ${x}^{2} \ge 0$
which implies ${x}^{2} - 9 \ge - 9$
giving $y = {x}^{2} - 9$ a minimum value of $\left(- 9\right)$ (and no limit on its maximum value.) That is it has a range from $\left(- 9\right)$ up to positive inifinite.