EXAMINING THE GRAPHS
We will examine the graphs beginning
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.
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.
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.