# What is the range of the function f(x) = x^2 + 3 if the domain is {-3, 0, 3}?

Jun 8, 2018

range $\left\{3 , 12\right\}$

#### Explanation:

If the domain is restricted to $\left\{- 3 , 0 , 3\right\}$ then we need to evaluate each term in the domain to find the range:

$f \left(x\right) = {x}^{2} + 3$

$f \left(- 3\right) = {x}^{2} + 3 = {\left(- 3\right)}^{2} + 3 = 12$

$f \left(0\right) = {x}^{2} + 3 = {0}^{2} + 3 = 3$

$f \left(3\right) = {x}^{2} + 3 = {3}^{2} + 3 = 12$

So the range is $\left\{3 , 12\right\}$