Even function And Odd function

Even function :

If f(-x)= f(x) ,then f is a even function ,which is related to symmetry about y-axis,if is replaced by -x and produces an equivalent equation.
For instance, the function f(x)=x^2 is even because

                              f(-x)=(-x)^2=x^2=f(x)
                

The geometric significance of an even function is that its graph is symmetric with respect to the y axis.This means that if we have plotted the graph of for x>=0 ,we obtain the entire graph simply by reflecting this portion about the
 y-axis.  Figure 19 shows..

Odd function :

If f(-x)= -f(x) ,then f is a odd function ,which is related to symmetry about the origin,if and only if replacing both x by -x and y by -y in its equation produces an equivalent equation.
For instance, the function f(x)=x^3 is odd because

                        f(-x)=(-x)^3=-x^3=-f(x)

The geometric significance of an odd function is that its graph is symmetric with respect to the origin.This means that if we have plotted the graph of for x>=0 ,

we obtain the entire graph simply by reflecting this portion about the origin.
Figure 20 shows..