The image is a problem about function transformations. The graph of $y = f(x)$ is given, and the task is to draw the graph of $y = -\frac{1}{2}f(x)$.

To solve this problem, we need to understand how the given transformation affects the original graph:

1. Reflection across the x-axis: The negative sign in $-\frac{1}{2}f(x)$ indicates a reflection over the x-axis. This means that every point on the graph of $f(x)$ will be mirrored across the x-axis.
2. Vertical compression by a factor of $\frac{1}{2}$: The factor $\frac{1}{2}$ indicates a vertical compression. This means that the y-coordinates of all points on the reflected graph will be halved.

Steps to Draw the Graph:

1. Identify the key points on the original graph $y = f(x)$. Let's assume we have points like $(x_1, y_1)$, $(x_2, y_2)$, etc.
2. Apply the reflection across the x-axis: Each point $(x_i, y_i)$ will become $(x_i, -y_i)$.
3. Apply the vertical compression: Multiply the y-coordinates by $\frac{1}{2}$. The reflected points will transform from $(x_i, -y_i)$ to $(x_i, -\frac{1}{2}y_i)$.

Applying the Transformation to Each Point:

• Take each point from the graph of $y = f(x)$ and apply the transformations described above.
• Plot these new points on the coordinate plane to draw the graph of $y = -\frac{1}{2}f(x)$.

Would you like a more detailed explanation or have any questions about this transformation process?

Here are some related questions to explore:

1. What happens if the transformation was $y = \frac{1}{2}f(x)$ instead?
2. How does a horizontal stretch or compression affect the graph?
3. What is the effect of a translation of the function, such as $y = f(x) + c$?
4. How would the transformation change if the expression was $y = -2f(x)$?
5. How can we determine the new range of the function after applying transformations?

Tip: Understanding each transformation (reflection, vertical/horizontal stretch, and translation) separately can help in combining them correctly to draw the transformed graph accurately.