# How do you find the range of  f(x) = 2x² if {-2, -2, 0, 1/2}?

Feb 6, 2018

The range is the set of y values

#### Explanation:

Simply plug in all of your domain (x) values into your equation and calculate each y value. Be sure to use parenthesis correctly.

Example: $2 {\left(- 2\right)}^{2} = 2 \cdot 4 = 8$

Feb 6, 2018

$y \in \left\{8 , 0 , \frac{1}{2}\right\}$

#### Explanation:

$\text{the range is the corresponding values of y for the }$
$\text{given values of x in the domain}$

$\text{domain is } x \in \left\{- 2 , 0 , \frac{1}{2}\right\}$

$\Rightarrow f \left(\textcolor{red}{- 2}\right) = 2 {\left(\textcolor{red}{- 2}\right)}^{2} = 2 \times 4 = 8$

$\Rightarrow f \left(\textcolor{red}{0}\right) = 2 {\left(\textcolor{red}{0}\right)}^{2} = 0$

$\Rightarrow f \left(\textcolor{red}{\frac{1}{2}}\right) = 2 {\left(\textcolor{red}{\frac{1}{2}}\right)}^{2} = 2 \times \frac{1}{4} = \frac{1}{2}$

$\text{range is } y \in \left\{8 , 0 , \frac{1}{2}\right\}$