A function f on R is an even function if for all x in the domain of f,

f(x) = f(-x).

Such a function is symmetric with respect to the y-axis when graphed.

If f is a polynomial function, then every exponent has to be even for the entire function to be even.

A function f on R is an odd function if for all x in the domain of f,

-f(x) = f(-x).

Such a function has rotational symmetry with respect to the origin.

If f is a polynomial function, then every exponent has to be odd for the entire function to be odd.

Examples

${\displaystyle x^2}$ is a even function but ${\displaystyle x^3}$ is odd. ${\displaystyle X^5 +56x+909}$ is neither.

${\displaystyle sin(x)}$ is odd while ${\displaystyle cos(x)}$ is even