# Graphs of Even and Odd Functions

Graphs of even and odd functions have following properties:

1. If function is even then its graph is symmetric about y-axis.
2. If function is odd then its graph is symmetric about origin.

Example 1. Draw graph of the function y=|x|.

Since f(-x)=|-x|=|x|=f(x) then function is even. This means that its graph is symmetric about y-axis.

If x>=0 then |x|=x, i.e. when x>=0 we have that y=x. Graph of the function y=x when x>=0 is bisector of first coordinate angle. Now draw it symmetrically about y-axis and you will obtain graph of the function y=|x|.

Example 2. Draw graph of the function y=x|x|.

Since f(-x)=(-x)|-x|=-x|x|=-f(x) then function is odd. This means that its graph is symmetric about origin.

If x>=0 then |x|=x, i.e. when x>=0 we have that y=x*x=x^2. Graph of the function y=x^2 when x>=0 is part of parabola. Now draw it symmetrically about origin and you will obtain graph of the function y=|x|.