Symmetry

Even

Odd

Facts about Symmetric Functions

• Most functions are neither even nor odd
• Any function symmetric about can be expressed as the sum of an even and odd component

Now let and let . Observe that . When we examine these two functions, we find that:

So is even, and

So is odd.

If we break the exponential function up into its even and odd components, we get

So we define the functions:

Which are she hyperbolic trigonometric functions