# Thread: Trying to find a function to represent my data

1. ## Trying to find a function to represent my data

Hello,

I'm trying to find the general form for a continuous function that will mimic the image I have attached. It is similar to a sigmoid function in the sense that it is flat initially and then has a very sharp transition, however it does not level out at the top, but rather increases continuously. Does anyone have any ideas as to what function may be appropriate?

2. ## Re: Trying to find a function to represent my data

Originally Posted by CLangford
I'm trying to find the general form for a continuous function that will mimic the image I have attached. It is similar to a sigmoid function in the sense that it is flat initially and then has a very sharp transition, however it does not level out at the top, but rather increases continuously. Does anyone have any ideas as to what function may be appropriate?
Here is a possibility.

3. ## Re: Trying to find a function to represent my data

That certainly looks promising. What was the form of the equation?

4. ## Re: Trying to find a function to represent my data

Originally Posted by CLangford
That certainly looks promising. What was the form of the equation?
$\[f(x) = \left\{ {\begin{array}{lr}{2\left( {\arctan (7) + 1} \right),}&{x < 4}\\{2\left( {\arctan (3x - 5) + 1} \right),}&{x \ge 4}\end{array}} \right.$
Now you can "play around" with those constants in the second condition.