Odd and Even Fnctioins

Some functions have symmetry about the origin.

If the function is such thatthen the graph of the function ihas reflectional symmetry in the y – axis and the function is said to be even.

If the function is such thatthen the graph of the function ihas rotational symmetry of order two about the origin and the function is said to be odd.

In the diagram belowis even andis odd.

It is not necessary for a function to be either even or odd.is neiher even or odd, but every function can be written as an even component plus and odd component.

Ifandthenis even andis odd, and

It is often quite easy to test a function for oddness or evenness.

sosois odd.

sosoandis even.

soorsois neither odd nor even.