***: NOTICE
The first equation has x and y intercepts at both positive and negative 1. (even power)
The second equation has x and y intercepts of positive 1 only. (odd power)
The third equation has has x and y intercepts at both positive and negative 1. (even power)
The fourth equation has has x and y intercepts of positive 1 only. (odd power)
We also notice that the odd or even powers indicate whether the graph will be closed or continous.
This might be helpful to see when we graph a few of them together.
Purple:
Red:
Blue:
Green:
Let's
look at 
One would assume that it would follow the pattern and have x and y intercepts at both positive and negative 1.
One would also assume that it is closed.
The assumption was correct.
One
would also assume that 
would follow the
pattern and have x and y intercepts at positive 1 only.
One would also assume that it is continuous.
Let's see:
This assumption was also correct.
Let' look at a linkto see the continous motion.
To generalize, will produce a graph with x and y intercepts at positive 1 only when n is odd. When n is even, a graph is produced with x and y intercepts at both positive and negative 1.