https://file.aiquickdraw.com/mathbot/file/1727025257839z66qzvj5.jpg

Let's break down the problem based on the graph and the function given:

### Problem Details:
- You are asked to use the graph of \( y = f(x) \) (on the left side) to graph the function \( g(x) = \frac{1}{2} f(x - 2) \).
- The operation \( g(x) = \frac{1}{2} f(x - 2) \) applies two transformations to the function \( f(x) \):
    1. **Horizontal Shift**: \( x - 2 \) shifts the graph 2 units to the right.
    2. **Vertical Compression**: \( \frac{1}{2} \) compresses the graph vertically by a factor of 2 (all y-values are halved).

### Applying Transformations:
1. **Horizontal Shift**: Move the entire graph of \( f(x) \) 2 units to the right.
2. **Vertical Compression**: For each y-value of the shifted graph, multiply it by \( \frac{1}{2} \).

### Observing the Graphs:
From the provided options (A, B, C, D), the graph that correctly applies both transformations is **B**. It shows:
- A shift 2 units to the right.
- All y-values compressed to half of their original values.

### Answer: The correct graph is **B**.

Would you like further clarification on the transformations or the solution process?

Here are five follow-up questions for more practice:
1. How would the graph of \( g(x) = 2f(x + 1) \) transform the graph of \( f(x) \)?
2. What effect does multiplying a function by a negative constant have on its graph?
3. How would \( g(x) = \frac{1}{3}f(x + 3) \) change the graph of \( f(x) \)?
4. What happens if you add a constant to \( f(x) \), like \( g(x) = f(x) + 3 \)?
5. Can you describe the transformation for \( g(x) = -f(x - 1) \)?

**Tip**: Always apply horizontal shifts before vertical stretches or compressions when analyzing 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.

Learn how to graph the transformed function g(x) = (1/2) f(x - 2) by applying horizontal shifts and vertical compressions. This problem involves function transformations, including shifting the graph 2 units to the right and compressing it vertically by a factor of 1/2. Suitable for high school students.

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