*****:
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.**