If f is an even function, which of the following describes f(-x)?

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Multiple Choice

If f is an even function, which of the following describes f(-x)?

Explanation:
Evenness means the graph is symmetric about the y-axis, so replacing x with -x does not change the value of the function. Therefore f(-x) = f(x) for every x in the domain. For example, if f(x) = x^2, then f(-x) = (-x)^2 = x^2 = f(x), illustrating the property. Other forms would describe different behavior: f(-x) = -f(x) would be odd symmetry, f(-x) = 0 would imply the function is zero for all x (a much stronger condition), and f(-x) = x would not reflect the outputs matching at x and -x.

Evenness means the graph is symmetric about the y-axis, so replacing x with -x does not change the value of the function. Therefore f(-x) = f(x) for every x in the domain. For example, if f(x) = x^2, then f(-x) = (-x)^2 = x^2 = f(x), illustrating the property.

Other forms would describe different behavior: f(-x) = -f(x) would be odd symmetry, f(-x) = 0 would imply the function is zero for all x (a much stronger condition), and f(-x) = x would not reflect the outputs matching at x and -x.

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