Answer
Domain: $[0, 2]$
Range: $[4, 24]$
Work Step by Step
The given function $f(x)=5x^2+4$ has its domain restricted to $0 \le x \le 2$.
Thus, its domain is $[0, 2]$.
Note that the value of the function $f(x)=5x+4$ is increasing from $x=0$ to $x=2$.
Thus, within its domain, the function's minimum value is at $x=0$, and its maximum value will be at $x=2$.
Find the value of $y$ when $x=0$ and when $x=2$ to have:
When x = 0,
$f(0)=5(0^2)+4=0+4=4$
When x = 2,
$f(2) = 5(2^2)+4 = 5(4)+4=20+4=24$
This means that the y-values of the function range from 4 to 24.
Therefore the range of the function is $[4, 24]$
