https://file.aiquickdraw.com/mathbot/file/172687220343373q7am1e.jpg

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?

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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!

Given the graph of y = f(x) shown below, what is the graph of y = -f(x)?

Understand how to transform the graph of y = f(x) to y = -f(x). This question involves reflecting the given function across the x-axis, making all positive y-values negative and vice versa. Suitable for high school students in Grades 9-12.

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