EVEN AND ODD FUNCTIONS

DEFINITION OF EVEN AND ODD FUNCTIONS
Even functions
If you let f(x) be a real-valued function of a real variable. Then you will get a equation that has the follow: f(−x) = f(x) (for all the real number of x ).
Even function graphs are always symmetrical with the y-axis.
Examples of even functions are x^2, x^4, x^6, cos(x) [even function includes only even powers]

Example use the cos (x):
f(-x) = -cos7(-x)
-cos (-7x)
-cos7x
f(-x) = f(x)

Example of graphs for Even Functions:

Odd Functions Again, let f(x) be a valued function of a real variable. Then if f is odd you will get the following equation: f(-x) = -f(x) (for all real numbers of x).
The odd function's graph is always be symmetric to the origin. Examples of odd functions are x, x^3, x^9, sin(x) [odd function includes only odd powers]

Example use sin (x):
f(-x) = sin (-3x)
-sin(3x)
f(-x) = -f (x)

Examples of graphs for Odd Functions: