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For a real-valued function $f(x)$, what does it mean for $f(x)$ to be an even function versus an odd function?

Study flashcard from the deck Gaokao essentials: original practice.

Answer

Even: $f(-x) = f(x)$ (symmetric about y-axis); Odd: $f(-x) = -f(x)$ (symmetric about origin).

Explanation

A standard consequence is that $\int_{-a}^a f(x)\,dx = 0$ for continuous odd functions, and $2\int_0^a f(x)\,dx$ for continuous even functions.

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