In this investigation we are asked to examine: for n in this case to be from -3 to +3.As n grows large the graph disconnects at the intersection of the ellipse like figure 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) . As noted, something very interesting happens when n =1 i.e . From the equation, it can be noted that there are two equations meeting at two points which is evidenced by the existence of the nods at the point of intersection. If the two equations meet then, they can be factorized so that more investigations can be made. Note that the equation can be factorized further i.e which means this equation is made of two equations which meet at given points as shown below.
To carry out more investigation , it is noted that the line Y = X intersect the equation which seems to looks like an ellipse centered at (0,0) with its intercepts at points (0,-1), (1,0), (0,1) and (-1,0). Click here to proof that the equation is ellipse. with center (0,0). For more illustration click Graphing calc #
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.