Even Functions and Odd Functions:

Even Functions and Odd Functions:

A function y = f(x) is an:

Evenfunction of x if f(-x) = f(x),

Odd function of x if f( -x) = - f(x),

for every xin the function s domain.

The graphs of evenand oddfunctions have characteristic symmetry properties.

The graph of an even function is symmetric about the y-axis.

The graph of an odd function is symmetric about the origin.


Example 4:
f(x)=x^2is an even function, since?(-x) ?^2=x^2 for all x, (symmetry about y-axis).

Example 5:
f(x)=x^3is an odd function, since?(-x) ?^3=-x^3 for all x, (symmetry about the origin).


Example 6:
f(x)=xis an odd function, since(-x)=-x for all x, (symmetry about the origin).


Example 7:
f(x)=x+1 is neither even nor odd:
Not even function since, f( -x)? f(x)for all x?0where f(-x)=(-x)+1,but f(x)=x +1.
Not odd function since, f(-x)?-f(x) where f(-x) =-x+1, but -f(x) =-x-1.

Example 8:
f(x)=cos?xis: an even function:cos?(-x)=cos?x for all x, (symmetry about y-axis).