by

**SOMIN KIM**

Explore the following equation for different values of

1) Examining the graph of

When **a** is a positive integer, the graphs ofare expressed like this.

We can see that from these graphs

When **a** is a positive decimal o<a<1, the graphs ofare expressed like this.

When **a** is a negative integer, the grafs ofare expressed like this.

When **a** is a negative decimal, the graphs ofare expressed like this.

There are animation graphs. We can see the change of graphs' shape as the value of **a **change at once.

Multiple Graphs.