Graphical interpretation of Even and Odd symmetry in functions.

An even function is one for which is true. Graphically, this suggests that if you pick any and get its value, then you will get the same value at , for all in the domain.
An odd function is one for which is true. Graphically, this suggests that if you pick any and get its value, then you will get the opposite 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 reflection of itself over the -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 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.