Appendix D - Graphing Techniques - Exercises - Page 446: 5i

Graph "B" is the correct sketching.

For $y = |x+2| - 2,$ when $x=0, y=0, x=-2, y=-2$ and $x=-4, y=0$ The curve passes through $(0,0), (-2,-2)$ and $(-4,0)$. Since the graph of $y=|x+2|-2$ is the same as the graph of $y=|x|$ but with a horizontal translation of 2 units to the left and a vertical translation of 2 units down, graph "B" is the correct sketching.