Appendix D - Graphing Techniques - Exercises - Page 449: 51

Refer to the curve in Black in Graph I

For $y = |x| - 1,$ when $x = 5, y = 4;$ $x = 3, y = 2;$ $x = 0, y = -1;$ $x = -3, y = 2;$ $x = -5, y = 4$ As seen, $y = |x| - 1$ is the vertical translation of $y = |x|$ down by 1 unit as well. Domain = $(−\infty, \infty)$ Range = $[-1, \infty)$