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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?

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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.

Translate the graph of y = |x| to make it the graph of y = |x + 4| - 2.

Learn how to translate the graph of y = |x| to y = |x + 4| - 2 by shifting the graph 4 units left and 2 units down. This transformation covers graph translation concepts in algebra, perfect for students in Grades 8-10.

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