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Odd and even functions
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Learn it A function is even if f(−x) = f(x) (symmetric in the y-axis, like x² and cos x). It is odd if f(−x) = −f(x) (rotational symmetry about the origin, like x³ and sin x). Many functions are neither.
Example: Is f(x) = x³ − 4x odd, even or neither?
- f(−x) = −x³ + 4x = −(x³ − 4x) = −f(x).
- So f is odd.
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