Answer
Refer to the curve in Black in Graph I
Work Step by Step
For $f(x) = \frac{1}{2}x^3 + 2$
when
$x = 2, y = 6;$
$x = 0, y = 2;$
$x = -2, y = -2;$
As seen, $f(x) = \frac{1}{2}x^3 + 2$ is the vertical shrinking by half and the vertical translation up by 2 units of $f(x) = x^3.$
Domain = $(-\infty, \infty)$
Range = $(-\infty, \infty)$
