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The problem asks to describe the transformations necessary to convert the graph of \( f(x) = |x| \) into that of \( g(x) = -|x| + 2 \).

### Step-by-step breakdown:

1. **Reflection**: The function \( f(x) = |x| \) produces a V-shaped graph that opens upwards. In \( g(x) = -|x| + 2 \), the negative sign in front of the absolute value reflects the graph across the **x-axis**. This changes the graph from opening upwards to opening downwards.

2. **Translation**: The "+2" outside the absolute value indicates a vertical translation. The entire graph is shifted **up by 2 units**.

### Conclusion:
The transformation involves reflecting the graph across the **x-axis** and then translating it **up 2 units**.

Thus, the correct answer is:
- **Reflect across the x-axis, translate up 2 units.**

Would you like further explanation or have any questions?

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Here are 5 related questions to deepen your understanding:
1. What kind of transformations affect the shape of a graph but not its position?
2. How do horizontal translations affect the equation of a graph?
3. How would the graph of \( g(x) = |x| - 2 \) compare to that of \( f(x) = |x| \)?
4. What would happen if the graph were reflected across the y-axis instead of the x-axis?
5. How would adding a coefficient in front of \( x \) inside the absolute value (e.g., \( f(x) = |2x| \)) affect the graph?

**Tip**: Always pay close attention to signs when dealing with reflections.

Describe the transformations necessary to transform the graph of f(x) = |x| into that of g(x) = -|x| + 2.

Learn how to transform the graph of f(x) = |x| into that of g(x) = -|x| + 2. This problem involves reflecting across the x-axis and translating up 2 units. Perfect for students in Grades 9-11 studying algebraic graph transformations.

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