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The question asks to identify the diagram that shows the graphs of both \( y = f(x) \) and \( y = f(-x) \).

- The function \( f(-x) \) reflects the graph of \( f(x) \) over the **y-axis**.
  
### Analysis of the graphs:
- We are looking for two graphs where one is the reflection of the other over the y-axis. This means, for each \( x \)-coordinate on the graph of \( f(x) \), the corresponding point on \( f(-x) \) should have the same y-coordinate but the opposite x-coordinate.

### Steps to find the correct graph:
1. Compare the given pairs of graphs.
2. Check for symmetry around the y-axis.
3. In the correct pair, one graph should be a mirror image of the other.

Based on this, the diagram that satisfies these conditions would be **D**. The two graphs in diagram D are mirrored over the y-axis.

Would you like further details on how to identify reflections or any other aspects of this problem? 

Here are some follow-up questions:
1. What is the effect of transforming a function \( f(x) \) to \( f(-x) \)?
2. How do transformations like \( f(x) + c \) affect the graph of a function?
3. What is the difference between even and odd functions?
4. How would you graphically identify if a function is odd or even?
5. How can you determine if a graph represents a reflection over the x-axis instead?

**Tip:** Whenever reflecting over the y-axis, every point on the graph should flip horizontally, keeping the y-values the same but switching the signs of the x-values.

Identify the diagram that shows the graphs of both y = f(x) and y = f(-x).

Learn how to identify the graphs of both y = f(x) and y = f(-x) by recognizing their symmetry over the y-axis. This problem covers key concepts such as graph reflections and function transformations, suitable for students in Grades 9-12.

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