https://file.aiquickdraw.com/mathbot/file/1726255194181rvpccwdw.jpg

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.

Use the graph of y = f(x) to graph the function g(x) = 1/2 * f(x - 2). Choose the correct graph of g from the options provided.

Learn how to graph the function g(x) = 1/2 * f(x - 2) by applying a horizontal shift and vertical compression to the original graph y = f(x). The correct answer involves shifting the graph 2 units to the right and compressing it vertically by a factor of 2.

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