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To transform the graph of \( y = |x| \) to match the graph of \( y = |x + 3| - 4 \), we apply two translations:

1. **Horizontal Shift:** The expression \( |x + 3| \) shifts the graph **3 units to the left**.
2. **Vertical Shift:** The \( -4 \) outside the absolute value shifts the graph **4 units down**.

So, to achieve this transformation, move the original graph of \( y = |x| \) **3 units left and 4 units down**.

Would you like further details on graph transformations?

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Here are some related questions to deepen your understanding:

1. How would the graph change if we used \( y = |x - 3| - 4 \) instead?
2. What effect does a positive constant outside the absolute value function have on the graph?
3. How do vertical stretches and compressions affect the graph of \( y = |x| \)?
4. What happens if we replace \( x \) with \( -x \) inside the absolute value function?
5. How would we graph \( y = |x + 3| + 4 \)?

**Tip:** When transforming graphs, focus on horizontal and vertical shifts first before considering stretches and reflections.

Translate the graph of y = |x| to make it the graph of y = |x + 3| - 4.

Learn how to translate the graph of y = |x| to match y = |x + 3| - 4. This involves shifting the graph 3 units left and 4 units down, demonstrating key concepts in absolute value transformations. Suitable for students in Grades 9-10.

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