Answer
See graph
Domain: $(-\infty,\infty)$
Range: $(-\infty,\infty)$
Work Step by Step
We are given the function:
$f(x)=(x-1)^3+2$
We start with the basic function $a(x)=x^3$.
We horizontally shift $a(x)$ one unit to the right to get $b(x)=(x-1)^3$.
Then we vertically shift $b(x)$ 2 units upward to get $f(x)=(x-1)^3+2$.
We use 3 points: $(0,1),(1,2),(2,3)$
The domain of $f$ is:
$D=(-\infty,\infty)$
The range of $f$ is:
$R=(-\infty,\infty)$
