The problem asks for the transformation applied to the function $f(x)$ to obtain $g(x)$, given their respective graphs.

Looking at the graphs:

• The graph of $g(x)$ appears to be a reflection of the graph of $f(x)$ over the x-axis. In other words, for each point on the graph of $f(x)$, the corresponding point on the graph of $g(x)$ has the same x-coordinate but an opposite y-coordinate.

This means the transformation is a vertical reflection, which mathematically can be written as:

$g(x) = -f(x)$

Therefore, the correct option is:

$g(x) = -f(x)$

Would you like further details on transformations? Here are 5 follow-up questions to explore the concept further:

1. What is the effect of reflecting a function over the y-axis instead of the x-axis?
2. How would shifting the graph of $f(x)$ affect its equation?
3. What happens if you apply multiple transformations, such as reflection and shifting?
4. How does the graph of $g(x) = f(-x)$ differ from $g(x) = -f(x)$?
5. Can we combine transformations into a single equation? If so, how?

Tip: A reflection over the x-axis changes the sign of the y-values of the function while keeping the x-values the same.