The problem asks to translate the graph of $y = |x|$ to make it the graph of $y = |x + 4| - 2$.

To break this down:

1. Horizontal Shift: The term $|x + 4|$ indicates a horizontal translation of the graph. The $+4$ inside the absolute value causes a shift 4 units to the left.

2. Vertical Shift: The term $-2$ outside the absolute value moves the entire graph 2 units down.

Thus, the transformation to go from the graph of $y = |x|$ to the graph of $y = |x + 4| - 2$ involves:

• Shifting the graph 4 units to the left.
• Shifting the graph 2 units downward.

Would you like a detailed step-by-step process on how to graph this transformation, or is there anything else you'd like to clarify?

Here are 5 related questions:

1. What effect does a constant inside the absolute value have on the graph's horizontal translation?
2. How does a constant outside the absolute value affect the vertical shift?
3. What is the vertex of the translated graph $y = |x + 4| - 2$?
4. How would the graph change if it was $y = |x - 4| + 2$ instead?
5. How do transformations affect the symmetry of absolute value graphs?

Tip: Always apply horizontal transformations before vertical ones when graphing functions.