Even/Odd Functions

A function is even if, for each x in the domain of f,  f(–x) = f(x).  Even functions have reflective symmetry across the y-axis.

Example of an even function:

   f(x) = x2
 f(–x) = (–x)2 = x2 = f(x)

        

 

A function is odd if, for each x in the domain of ff(–x) = –f(x).  Odd functions have 180º rotational symmetry about the origin.    

Example of an odd function:

    f(x) = x3
f(–x) = (–x)3 = –x3 = –f(x)