The problem is asking to graph the function $g(x) = \frac{1}{2} f(x - 2)$ using the provided graph of $y = f(x)$.

Here’s how we approach it:

1. Horizontal Shift: The expression $f(x - 2)$ indicates a horizontal shift. Specifically, the graph of $f(x)$ is shifted 2 units to the right.

2. Vertical Compression: The coefficient $\frac{1}{2}$ outside the function means the graph undergoes a vertical compression by a factor of 2. This makes the graph half as tall as the original.

Steps to transform the graph:

• Shift the graph 2 units to the right.
• Vertically compress the graph, halving the height of each point.

Now, analyzing the options:

• Option A shows a vertically compressed graph, but it is not shifted.
• Option B shows the correct shift of 2 units right and a correct vertical compression.
• Option C does not show the correct shift or compression.
• Option D shows a shift, but it is not vertically compressed correctly.

Thus, Option B is the correct graph of $g(x)$.

Would you like more details or explanations?

Here are 5 related questions to expand on the concept:

1. What is the effect of a horizontal shift on any function?
2. How does vertical compression/stretching affect the graph of a function?
3. What happens if you apply a negative coefficient to a function (e.g., $-f(x)$)?
4. How would you graph $f(x + 2)$ instead of $f(x - 2)$?
5. How can you describe the transformation of $f(x)$ using a table of values?

Tip: Always apply horizontal shifts before vertical transformations when working with composite transformations.