# How do you find the domain and range for y=x^2=9?

Jun 5, 2015

As written
$\textcolor{w h i t e}{\text{XXXX}}$Since ${x}^{2} = 9 \rightarrow x = \pm 3$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$the Domain is $\left\{- 3 , + 3\right\}$
$\textcolor{w h i t e}{\text{XXXX}}$and since $y = x$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$the Range is also $\left\{- 3 , + 3\right\}$

Probable Intended equation: $y = {x}^{2} - 9$
$\textcolor{w h i t e}{\text{XXXX}}$In this case the equation is defined for all Real values of $x$,
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$ so the Domain is $x \epsilon \mathbb{R}$
$\textcolor{w h i t e}{\text{XXXX}}$the minimum value for $y$ is $y = - 9$,
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$so the Range is $y \epsilon \left[- 9 , + \infty\right)$