The task involves matching transformations of the function $f(x)$ with their corresponding graphs. Here’s how the transformations generally affect the graph:

1. $f(x) - 2$: Shifts the graph 2 units down.
2. $f(2x)$: Compresses the graph horizontally by a factor of 2.
3. $-f(x+2)$: Reflects the graph over the x-axis and shifts it 2 units left.
4. $2f(-x)$: Reflects the graph over the y-axis and stretches it vertically by a factor of 2.
5. $f(x)/2$: Compresses the graph vertically by a factor of 2.
6. $f(x-2)$: Shifts the graph 2 units right.
7. $-f(x/2)$: Stretches the graph horizontally by a factor of 2 and reflects it over the x-axis.
8. $f(-x) + 2$: Reflects the graph over the y-axis and shifts it 2 units up.
9. $2f(x) - 2$: Stretches the graph vertically by a factor of 2 and shifts it 2 units down.

I will now match these transformations with the graphs shown in the image. Here's the matching list:

1. $f(x) - 2$ → Graph I (shifted down)
2. $f(2x)$ → Graph C (horizontal compression)
3. $-f(x + 2)$ → Graph E (reflection and left shift)
4. $2f(-x)$ → Graph D (reflection over y-axis and vertical stretch)
5. $f(x) / 2$ → Graph A (vertical compression)
6. $f(x - 2)$ → Graph H (shifted right)
7. $-f(x / 2)$ → Graph F (horizontal stretch and reflection)
8. $f(-x) + 2$ → Graph G (reflection over y-axis and shifted up)
9. $2f(x) - 2$ → Graph B (vertical stretch and downward shift)

Would you like more details on how each transformation affects the graph? Here are some related questions to explore further:

1. How does a vertical shift differ from a horizontal shift in graph transformations?
2. Why does compressing a function horizontally involve multiplying $x$ by a constant greater than 1?
3. How does reflecting a graph over the y-axis change the function's equation?
4. What is the effect of stretching or compressing a function vertically?
5. Can you explain how multiple transformations are applied step by step to a function?

Tip: When working with transformations, always apply horizontal changes (inside the function) before vertical ones for accurate graphing!