To answer the question, let’s analyze the given function transformation:

The function $g(x) = -5f(x)$ can be broken into two transformations of $f(x)$:

1. The factor $-5$:
   • The negative sign ($-$) reflects the graph of $f(x)$ over the $x$-axis.
   • The factor $5$ is a vertical dilation (stretch) of the graph by a scale factor of $5$.

Which answer choice matches this?

• Horizontal dilations affect the $x$-axis (incorrect here).
• Vertical dilations and reflections over the $x$-axis describe the transformation properly.

Thus, the correct answer is:

D) The graph of $y = g(x)$ is a vertical dilation of the graph of $y = f(x)$ by a scale factor of 5, followed by a reflection over the $x$-axis.

Do you need further clarification or steps? Let me know!

Here are 5 related questions to deepen your understanding:

1. How would $g(x) = 5f(x)$ transform the graph of $f(x)$?
2. What happens to a graph if the transformation is $g(x) = f(-x)$?
3. How would you describe a horizontal compression by a factor of 2?
4. How do you reflect a graph across the $y$-axis?
5. If $g(x) = -\frac{1}{2}f(x)$, what transformations occur?

Tip: Vertical dilation affects the $y$-values, while reflections depend on the sign of the coefficient.