Assignment 1

Paula Whitmire



We will examine the graphs beginning with

This is a graph of a circle with the origin as its center.

Now we will graph


We no longer have a circle. We have a curve passing through points (1,0) and (0,1). It is like one fourth of a circle with the origin as its center is there and the other three fourths is pulled away from the origin. Now observe the graph of

With the power of 4 the curve is once again centered about the origin. It is not a circle however. Let us use several more even powers and observe the graphs.


 Color Exponent
Purple 4
Red 6
Blue 12
Lime Green 24
Light Blue 40

The larger the even exponent the curve becomes more square like in shape. When the power became 40 there was not much change from the exponent of 24. We suppose that as the even power gets larger the figure will be even more square like. The figures all pass through the points (1,0), (0,1), (-1,0) and (0,-1).Now we will explore larger odd exponents.

 Color Exponent
 Purple  3
Red 5
Blue 13
Lime Green 23
Light Blue 41

These graphs appear as half ( -1 < x < 1 ) of the square like figure with the other half ( x < -1 or x > 1) turning away from the origin. It appears that the line y=-x is an assymptote. It is assumed that the larger the odd exponent the more square shaped the figure becomes from -1 < x < 1.