Answer
Refer to the curve in Black in Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/89f5df44-d4e2-4d09-8383-4e22e591820d/result_image/1506960731.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011838Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=5e9e32886d6de0415bf29f766d65821502b9c862cfcb0077d9d71107042fe986)
Work Step by Step
For $f(x) = \frac{1}{2}x^3 - 4$
when
$x = 2, y = 0;$
$x = 0, y = -4;$
$x = -2, y = -8;$
As seen, $f(x) = \frac{1}{2}x^3 - 4$ is the vertical shrinking by half and the vertical translation down by 4 units of $f(x) = x^3.$
Domain = $(-\infty, \infty)$
Range = $(-\infty, \infty)$