Answer
Refer to the curve in Black in Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c19714bc-5925-42ac-ae06-8e58bd6e49a9/result_image/1506960958.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020548Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=9e90b75335b035741701490750443475096247494e14c978c9e1fe754df5ebaf)
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 = $(-\infty, \infty)$