# Even & Odd Functions

- Author:
- Ken Schwartz

- Topic:
- Functions

Graphical interpretation of Even and Odd symmetry in functions.

An is true. Graphically, this suggests that if you pick any and get its value, then you will get the value at , for all in the domain.
An is true. Graphically, this suggests that if you pick any and get its value, then you will get the value at , for all in the domain.
You can test this for the graphed functions by comparing the values of with the values of and . If they match for all , then is even or odd, respectively.
In simpler terms, an even function's graph is a -axis. If you check the "Reflect f(x)" box, 's reflection will be drawn in yellow. If the yellow reflection and the original (black) function overlap everywhere, then the function is even.
An odd function's graph is a 180-degree

*even function*is one for which*same**odd function*is one for which*opposite**reflection*of itself over the*rotation*of itself around the origin. If you check the "Rotate f(x)" box, a blue copy of the graph will rotate 180 degrees about the origin. If the blue rotation and the original (black) function overlap everywhere, then the function is odd.