The problem in your image asks for the transformations needed to graph the function $h(x) = |x + 2| - 5$ from the absolute value function $f(x) = |x|$.

To analyze the transformations:

1. Horizontal Shift: The term $|x + 2|$ indicates a horizontal shift. Since $+2$ inside the absolute value moves the graph to the left, this is a horizontal shift 2 units to the left.

2. Vertical Shift: The term $-5$ outside the absolute value shifts the graph vertically. This is a vertical shift 5 units down.

There are no stretches, shrinks, or reflections in this case because there are no coefficients modifying $x$ or $|x|$ directly.

Correct choices:

• D. Horizontal shift (left by 2 units)
• F. Vertical shift (down by 5 units)

Let me know if you want more details on this or have any questions!

Here are five follow-up questions to explore this concept further:

1. What is the effect of multiplying the function $f(x) = |x|$ by a negative constant?
2. How would the graph change if the function were $h(x) = 2|x + 2| - 5$?
3. What transformation would occur if $h(x) = |x + 2| + 5$?
4. How would a reflection over the y-axis be represented in the absolute value function?
5. What happens to the graph of $f(x) = |x|$ if we add a constant inside the absolute value?

Tip: Always remember that transformations inside the absolute value affect the graph horizontally (left/right), and those outside affect it vertically (up/down).