Answer
See graph
Domain: $[-3,3]$
Range: $[0,27]$
Work Step by Step
We are given the function:
$f(x)=(9-x^2)^{3/2}=\sqrt{(9-x^2)^3}$.
Graph the function using the window [-4,4]X[0,30].
The domain of the function consists in the values of $x$ for which the function makes sense. The order of the radical being even, we have:
$9-x^2\geq 0\Rightarrow x\in [-3,3]$.
The domain is $D=[-3,3]$.
The range is the set of values that the function can take.
The minimum value of the function corresponds to $x=3$ and is 0 and the maximum corresponds to $x=0$:
$f(0)=\sqrt{(9-0^2)^3}=\sqrt {3^6}=3^3=9$.
The range is $R=[0,27]$.
