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Math Help - Trying to find a function to represent my data

  1. #1
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    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?

    Thank you for your help.

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

    Quote Originally Posted by CLangford View Post
    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?
    Click image for larger version. 

Name:	Function.png 
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ID:	24479
    Here is a possibility.
    Attached Thumbnails Attached Thumbnails Trying to find a function to represent my data-untitled.gif  
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  3. #3
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    Re: Trying to find a function to represent my data

    That certainly looks promising. What was the form of the equation?
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    Re: Trying to find a function to represent my data

    Quote Originally Posted by CLangford View Post
    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.
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