Answer
Refer to the curve in Black in Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c558577c-51b8-4cd8-8a00-19f1a2f2325e/result_image/1506956785.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012229Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=30d059e2a4aa5351672b1cdb1813cdcbb8525e0d193b03ee4ad9d04f5176935c)
Work Step by Step
For $y = -(x - 1)^3,$
when
$x = 3, y = -8;$
$x = 2, y = -1;$
$x = 1, y = 0;$
$x = 0, y = 1;$
$x = -1, y = 8$
As seen, $y = -(x - 1)^3$ is the horizontal translation of $y = x^3$ to the right by 1 unit and then reflected across the $x$-axis as well.
Domain = $(−\infty, \infty)$
Range = $(-\infty, \infty)$