Even and Odd Funtions

Here are some even numbers:
2, 4, 6

Here are some odd numbers:
1, 3, 5

Here are some that aren't even or odd:



So how do we determine if a function is even or odd?


A function f is even if, for each x in the domain of f, f(-x) = f(x)
f(-x) = f(x)

Example:

f(x) = - 7
f(x) = (-) - 7
- 7 even (same as the original function)

A function f is odd if, for each x in the domain of f, f(-x) = -f(x)
f(-x) = -f(x)

Example:
f(x) = - 4x
f(-x) = (-x)^3-4(-x)

=-x^3 + 4x

Then prove it's odd
-f(x) = -1 (x^3 - 4x)
= -x^3 + 4X
(same as f (-x))