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The problem involves identifying the correct graph transformation based on the given function \( f(x) \), which is shown in Figure 1. The task is to find the graph of \( |f(|x| - 2)| + 2 \) among the provided figures.

### Step-by-Step Solution:

1. **Absolute Value Inside**: The expression \( |x| - 2 \) reflects the graph of \( f(x) \) about the y-axis (making it symmetric with respect to the y-axis) and then shifts it 2 units to the right. 

2. **Absolute Value Outside**: The expression \( |f(|x| - 2)| \) takes the absolute value of the function's output, meaning all negative values of the function will be flipped to positive. This results in only non-negative y-values in the graph.

3. **Vertical Shift**: Finally, adding 2 to the entire function \( |f(|x| - 2)| + 2 \) shifts the entire graph up by 2 units.

Considering these transformations, we look for the figure that shows:
- Symmetry with respect to the y-axis.
- A horizontal shift to the right by 2 units.
- No negative values on the y-axis (all values are above or on the x-axis).
- The graph has been shifted up by 2 units.

After analyzing the provided graphs, the correct transformation corresponds to **Figure 7**. Figure 7 shows a graph that is symmetric about the y-axis, shifted right by 2 units, has no negative y-values, and is shifted upwards by 2 units.

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Would you like more details or have any questions? Here are some related questions you might find useful:

1. What effect does the absolute value have on a graph?
2. How do vertical and horizontal shifts affect the graph of a function?
3. What are the effects of combining multiple transformations on a graph?
4. How do you reflect a function across the y-axis?
5. What are some common mistakes when interpreting function transformations?

**Tip:** When transforming functions, always handle operations inside the function first (horizontal transformations), then outside the function (vertical transformations).

Given the function f(x) with the graph shown in Figure 1, determine which figure represents the graph of |f(|x| - 2)| + 2.

Understand how to transform the function f(x) into |f(|x| - 2)| + 2 by analyzing graph transformations such as absolute value and shifting. Suitable for students in Grades 10-12.

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