# How do you find the range of h(x)=x^2 -4 for the domain (-2,0,3,8)?

Dec 23, 2016

$\left\{- 4 , 0 , 5 , 60\right\}$

#### Explanation:

The domain of a function is the set of all allowed inputs. The range of the function is the set of all possible outputs, that is, the set of all values obtained by applying the function to elements of the domain.

To find the range of $h \left(x\right)$, then, we apply it to each element of the domain:

$h \left(- 2\right) = {\left(- 2\right)}^{2} - 4 = 0$
$h \left(0\right) = {0}^{2} - 4 = - 4$
$h \left(3\right) = {3}^{2} - 4 = 5$
$h \left(8\right) = {8}^{2} - 4 = 60$

So the set of all values which can be obtained by applying $h \left(x\right)$ to an element of its domain is $\left\{- 4 , 0 , 5 , 60\right\}$, and thus that is the range of $h \left(x\right)$.