Power Function

A function of the from f(x)=x^n is called a power function.
There n is a rational real number .
 The domain of power functions depend on the value of n.
 Such as
 f(x)=x^n

         f(x)=x^2
             Domain=R

         f(x)=x^(1/2)=Sqrt[x]
             Domain=[0,+infinity)

         f(x)=x^(-1)
             Domain =R-{0}

When n is a positive integer
The graphs of f(x)=x^n for n=1,2,3,4  and 5 are shown below. (These are polynomials with only one term.)

The general shape of the graph of f(x)=x^n depends on whether n is even or odd.If n is even, then f(x)=x^n is an even function and its graph is similar to the parabola f((x)=x^2. If n is odd, then f(x)=x^n is an odd function and its graph is similar to that of f((x)=x^3.


when 1/n , where n is positive integer
  its   called Root function.

when n = -1
its called reciprocal function.