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Let's analyze the given function step-by-step.

The base function is \( f(x) = |x| \).

The transformed function is \( h(x) = -|x - 2| \).

We need to identify the transformations applied to \( f(x) \) to obtain \( h(x) \).

### Transformations:
1. **Horizontal shift**: The expression \( |x - 2| \) indicates a horizontal shift to the right by 2 units.
   
2. **Reflection about the x-axis**: The negative sign in front of the absolute value, \( -|x - 2| \), reflects the graph over the x-axis, flipping it upside down.

Now, let's match these transformations to the choices provided:

- **A. Horizontal shift**: Yes, right by 2 units.
- **E. Reflection about the x-axis**: Yes, the negative sign reflects it over the x-axis.

### Final Answer:
The transformations needed are:
- A. Horizontal shift
- E. Reflection about the x-axis

Would you like further details or have any questions?

### Related Questions:
1. How would the graph change if the equation was \( h(x) = |x + 2| \)?
2. What transformation corresponds to \( h(x) = 2|x - 2| \)?
3. How does a vertical shift affect the graph of an absolute value function?
4. What happens to the graph of \( f(x) = |x| \) when reflected over the y-axis?
5. How does the slope of the arms of the graph change when there's a vertical stretch?

### Tip:
When analyzing transformations, always pay attention to signs inside the absolute value and in front of the function, as they indicate shifts and reflections.

What transformations are needed in order to obtain the graph of h(x) = -|x - 2| from the graph of f(x) = |x|?

Learn how to transform the absolute value function f(x) = |x| to the new function h(x) = -|x - 2|. This problem covers graph transformations, including horizontal shifts and reflections over the x-axis. Suitable for high school students (Grades 9-12).

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