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.