Even and odd functions [1.8]

Even function

Symbolically: An even function obeys: $$f(-x)=f(x).$$

Graphically:

The function to the left of the $y$ axis is the reflection about the $y$ axis of the function to the right of the $y$ axis.

Also called a symmetric function.

Odd function

Symbolically: An odd function obeys: $$f(-x)=-f(x).$$

Graphically:

The function to the left of the $y$ axis is the reflection through the origin of the function to the right of the $y$ axis.

Also called an anti-symmetric function.