HomeHelpContact usBack

Modules Open College - e-Learning Content Library
 
 
Even and uneven functions
 


Function f(x) is called even function if f(x) = f(-x) for every x from the function domain. A graph of even function is axis OY symmetrical to. Functions cos(x) or x2 are examples of even functions.

Function f(x) is called uneven function if f(x) = - f(-x) for every x from the function domain. A graph of uneven function is point of origin symmetrical to. Functions sin(x) or x3 are examples of uneven functions.

Some functions are neither even nor uneven, x3+1 as an example.

If the function f(x) domain is the point of origin symmetrical then the function is a sum of even and uneven functions f(x) = fe(x) + fu(x).

fe(x) = [f(x) + f(-x)]/2

fu(x) = [f(x) - f(-x)]/2

The model illustrates this theorem. You may insert a function into a text field f(x) and obtain its graph (blue) and graphs of corresponding even (red) and uneven (green) functions.



 
© OpenTeach Software, 2007