Using Graphing Calculator 3.2 to investigate
I graphed the four equations below.
The purple circle corresponds with
And the blue graph that looks more like a square than a circle corresponds with the equation
So the odd number powers graph to curve around the upper right hand corner of the square and circular graphs.
Here n= 2, 3, 4, 5
This leads me to believe that
will be closer to a square shape than the other even powered equations. This is verified in the table below.
fits around the upper right hand corner.
This relationship between even and odd powers continues with the graphs becoming more angular and square as the numerical value of the powers increase.