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The question asks: 

If \( f \) is a function with the property that \( f(-x) = f(x) \) for all values of \( x \), which statement must be true?

This property \( f(-x) = f(x) \) defines an **even function**. A function is even if its graph is symmetric about the **y-axis**. Based on this definition, we can conclude that the correct answer is:

**A. The graph of \( f \) is symmetric to the y-axis.**

Would you like further details, or do you have any questions?

Here are 5 related questions for further practice:
1. What is the definition of an odd function?
2. How do you determine if a function is symmetric about the origin?
3. Can a function be both even and odd? Explain why or why not.
4. What is the graphical interpretation of the inverse of a function?
5. How do transformations affect the symmetry of a function?

**Tip:** Even functions have symmetry about the y-axis, while odd functions have symmetry about the origin.

If f is a function with the property that f(-x) = f(x) for all values of x, which statement must be true?

Learn about even functions and how their graphs are symmetric about the y-axis. This problem demonstrates the core property f(-x) = f(x), providing insight into graph behavior and symmetry concepts in higher-level algebra. Suitable for Grades 9-12.

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