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.