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.