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# Odd and even functions

A numerical function is even if its graph is symmetric across the $y$-axis. Analytically, this means that, for all $x$, $$f(-x) = f(x).$$

Examples of even functions are $x^2$, $\cos(x)$, $\vert x\vert$.

A numerical function is odd if its graph has rotational symmetry of angle $\pi$ about the origin. Analytically, this means that, for all $x$, $$f(-x) = - f(x).$$

Examples of odd functions are $x$, $x^3$, $\sin(x)$ and $\tan(x)$.

Parity is the property of being either odd or even for a function.

Some functions are neither even nor odd, such as $x^2 - 3$