## EMAT 6680 Assignment #1

## Graphing Functions With Graphing Calculator

#### by Kent Wiginton

Assignment 1

1. In this investigation we are asked to examine:

When we substitute n for 4 in the equation something very interesting
happens when n=1.

The graph looks like an ellipse centered at (0,0) with the
line y=x running through it. As n grows large the graph disconnects
at the intersection of the ellipse and the line. Also the graph
becomes very curvy. As n gets very negative the graph looks as
if it is trying to straighten out, however it is "pined down"
at (0,1) and (0,-1). Here is a movie that will help to show exactly
what I am describing.

**See movie.**

What will happen when we decide to add a constant to each side
of the graph?

When we add a constant to each side of the equation we will
get different slices through the 3-dimensional surface given by
the equation

Take a look at the graph of this surface.

**Return**