Assignment #1 Nicole Mosteller EMAT 6680
Assignment #1 Nicole Mosteller EMAT 6680
To investigate
the relation for values of a and b greater than
0, I have chosen three graphs that best exemplify the changes
that occur when a and b are altered.
Figure 1: Let
a = 16 and b = 9.
Notice in Figure 1 that when a and b are square numbers (16 and 9, respectively), the intercepts are integer values. Although other values for a and b may not produce integer intercepts, the graphs will continue to be symmetric about the origin (see Figure 2).
Also notice the another difference between Figure 1 and Figure 2. In Figure 1, the value of a is greater than the value of b. Figure 2 demonstrates when the value of a is less than the value of b. Notice that the change in these values causes the middle of the graph to invert.
Figure 2: Let a = 10 and b = 15.
Figure 3: Let a = 0.25 and b = 0.6.
When comparing Figure 2 and Figure
3, we notice that the graphs are basically the same shape,
and all that has been altered is the size. The curves near the
origin have merely become smaller. Likewise, the same inversion
of the curves near the origin occurs when the value of a
is less than the value of b.
If the difference
in a and b causes the graph to invert near the origin,
what occurs when a and b are the same? This question
leads us to our next part of Investigation #1 - investigate
when a and b are equal to 1.