Appendix D - Graphing Techniques - Exercises - Page 449: 54

Refer to the curve in Black in Graph I

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 = $(-\infty, \infty)$