Graph the following: x2 + y2 = 1
Notice the circle has a radius of 1. It is a regular shape.
Now examine the graph: x3 + y3 = 1
The equation has now changed from a circle to a line with a rounded shape between the coordinates (-1,1) and (1,-1).
Let's increase the exponents again and graph x4 + y4 =1
The graph now exhibits the shape of a square with s=1.
How will an exponent of 5 changed the graph?
Let's examine it. Graph x5 + y5 = 1.
The graph now looks very similar to x3 + y3 = 1. It is a line with an interruption around (-1, 1) and (1, -1).
Now lets examine all the graphs together.
x2 + y2 = 1
x3 + y3 = 1
x4 + y4 =1
x5 + y5 = 1
Notice the points at x = 1, -1 and y = 1, -1. What can you assume from the graph of x24 + y24 =1? Or x25 + y25 =1?
Lets try even higher exponential values.
x100 + y100 =1
x101 + y101 =1
We can now justify an assumption that as the exponents get higher the image becomes sharper.
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