Explorations With Some Exponential Functions
by Oktay Mercimek
I will investigate some exponential functions like
, where c is from 2 to 25.
When c is 2, It is well known that is a circle.
If c is 3, then function is and its graph is
.
For , graph is
For , graph is
After these graphs, I have a feeling about a difference between odd c values and even c values.
I want to look at some even c values first.
Do you imagine what will happen when c is 1000?
It is not difficult to say it will seem like a square.
Let's look at some odd ones
I will add x=-y (yellow line) to show you some similarity.
little closer look to graph
When c is odd , x>0 and y>0, It tend to behave similar to ones that c is even.
For x<-1 ,y>1 and for x>1, y<-1 , It is very near to x=-y line.
After this investigations,We have learned that similar exponential functions don't have similar graphs and being odd or even is a key to understand the behavior of exponential function.