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This problem trains for: AMC-10, AMC-12, AIME.

A polynomial function f(x) satisfies the following condition for any real x, y:

equation

Which of the following statements are true?

Because the condition is true for any real value of x, y then substitute x=y:

equation

This means that f is a constant function, which implies that it is even and that it has an infinity of axes of symmetry.