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.
A bigger question here
would be: Is there a limit when the curves no longer get more angular and
square?