Assignment #1

Kristin Karas

Number 6

***: 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.