Appendix D - Graphing Techniques - Exercises - Page 449: 52

Refer to the curve in Black in Graph I

For $y = |x + 3| + 2,$ when $x = 1, y = 6;$ $x = -1, y = 4;$ $x = -3, y = 2;$ $x = -5, y = 4;$ $x = -7, y = 6$ As seen, $y = |x + 3| + 2$ is the horizontal translation to the left by 3 units and vertical translation up by 2 units of $y = |x|$ as well. Domain = $(−\infty, \infty)$ Range = $[2, \infty)$