Let's analyze the problem you provided.

The question asks for the transformations required to convert the graph of the function $f(x) = |x|$ into the function $h(x) = -|x + 2|$.

We start by recognizing the structure of $h(x)$: $h(x) = -|x + 2|$

Transformations:

1. Reflection about the x-axis:

   • The negative sign outside the absolute value, $-|x + 2|$, indicates a reflection of the graph of $f(x) = |x|$ over the x-axis. So this transformation applies.

2. Horizontal shift:

   • The $+2$ inside the absolute value, $|x + 2|$, indicates a horizontal shift to the left by 2 units. So a horizontal shift is applied.

There are no vertical shifts, stretches, or reflections about the y-axis involved.

The correct transformations are:

• A: Reflection about the x-axis
• E: Horizontal shift (left by 2 units)

Thus, the correct selections would be:

• A. Reflection about the x-axis
• E. Horizontal shift

Let me know if you would like more details or explanations on any step.

Here are 5 related questions you might explore:

1. How would the graph change if the function was $h(x) = |x + 2|$ instead of $-|x + 2|$?
2. What effect does adding a constant outside the absolute value, like $h(x) = |x| + 3$, have on the graph?
3. How does a vertical stretch or shrink affect an absolute value graph?
4. What is the effect of reflecting a graph about the y-axis?
5. How can you determine the vertex of the graph of $h(x) = -|x + 2|$?

Tip: Always identify the order of transformations when graphing functions, as some transformations can affect others (e.g., reflections and shifts).