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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 $$x^2 - 3$$