# Trying to find a function to represent my data

• Aug 9th 2012, 01:49 PM
CLangford
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?

Attachment 24479
• Aug 9th 2012, 02:26 PM
Plato
Re: Trying to find a function to represent my data
Quote:

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?
Attachment 24479

Here is a possibility.
• Aug 9th 2012, 02:52 PM
CLangford
Re: Trying to find a function to represent my data
That certainly looks promising. What was the form of the equation?
• Aug 9th 2012, 03:11 PM
Plato
Re: Trying to find a function to represent my data
Quote:

Originally Posted by CLangford
That certainly looks promising. What was the form of the equation?

$\displaystyle \[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.