https://file.aiquickdraw.com/mathbot/file/1726100819142hjcz5ib5.jpg

The problem asks to draw the graph of \( y = -\frac{1}{2} f(x) \), given the graph of \( y = f(x) \).

Here’s how the transformation works:

1. **Vertical Scaling (by \( \frac{1}{2} \))**: The factor \( \frac{1}{2} \) will compress the graph vertically. This means that every point on the graph of \( f(x) \) will be halved in the vertical direction. For example, if a point on the original graph is \( (x, y) \), the corresponding point on the transformed graph will be \( (x, \frac{y}{2}) \).

2. **Reflection (due to the negative sign)**: The negative sign will reflect the graph across the x-axis. So after compressing the graph, all positive values of \( y \) will become negative, and negative values will become positive. If a point on the compressed graph is \( (x, \frac{y}{2}) \), the reflected point will be \( (x, -\frac{y}{2}) \).

### Step-by-Step Instructions for Plotting:
- Take the original graph of \( f(x) \) and identify key points.
- Halve the \( y \)-coordinates (vertical compression).
- Reflect these new points across the x-axis.

Would you like more details, or help drawing the graph itself?

Here are 5 related questions:
1. What does a horizontal stretch or compression do to a graph?
2. How would you graph \( y = f(x + 2) \) compared to \( y = f(x) \)?
3. What is the effect of multiplying \( f(x) \) by \( 3 \) instead of \( \frac{1}{2} \)?
4. How do vertical shifts affect the graph of a function?
5. How does combining transformations (e.g., scaling and translating) work?

**Tip**: Always perform vertical transformations (scaling and reflecting) before horizontal ones, unless otherwise specified.

The graph of y = f(x) is shown. Draw the graph of y = -1/2 * f(x).

Understand how to transform the graph of y = f(x) to y = -1/2 * f(x) by applying vertical scaling and reflection. This problem covers key mathematical concepts, including graph transformations and function manipulation. Suitable for high school students.

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