Answer
Domain: $[0,2]$
Range: $[4,24]$
Work Step by Step
We are given:
$f(x)=5x^{2}+4, 0\leq x\leq 2$
The domain consists of all values that $x$ is allowed to be. In this case, $x$ is restricted to fall between $0$ and $2$, so the domain is: $[0, 2]$.
The range consists of all values that $y$ can be. We find the extremes of $y$ by using the end points of $x$ (this works because the equation is a parabola):
$f(0)=5(0)^{2}+4=4$
$f(2)=5(2)^{2}+4=24$
Thus the range is: $[4, 24]$.
