The question asks you to find the graph of $y = -f(x)$ based on the given graph of $y = f(x)$.

Concept:

The transformation $y = -f(x)$ reflects the graph of $f(x)$ over the x-axis. This means that every point $(x, y)$ on the graph of $f(x)$ will be transformed to $(x, -y)$ on the graph of $-f(x)$.

Steps to solve:

• The graph of $f(x)$ is already provided. We now need to reflect it across the x-axis to get $-f(x)$.
• Identify the points on the graph of $f(x)$, particularly where the function is positive or negative.
  • Any point where $f(x)$ is positive will now be negative in $-f(x)$.
  • Any point where $f(x)$ is negative will now be positive in $-f(x)$.

Looking at the provided answer choices:

• The correct graph should be the one where all positive y-values in the original graph are reflected below the x-axis, and all negative y-values are reflected above the x-axis.

From your uploaded image, the third option is correct. This graph shows the reflection of the original function across the x-axis.

Would you like further details or have any questions about this reflection?

Here are 5 related questions to explore:

1. How would the graph of $y = f(-x)$ differ from $y = f(x)$?
2. What happens when both reflections $y = -f(-x)$ are applied?
3. How do vertical shifts affect the graph of $y = f(x)$?
4. What is the effect of multiplying $f(x)$ by a constant greater than 1?
5. Can you describe the reflection for $y = -2f(x)$?

Tip: Reflecting over the x-axis simply inverts all y-values; positive becomes negative, and negative becomes positive!