in other programs, there is a possibility to take a data set and to find the function which fits best. Is there also such a possibility in Mathematica?

I only could find LinearModelFit or NonlinearModelFit, where you have to give the function.

For example, I want to find the best function for the following data plot: enter image description here

How to find it?

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    $\begingroup$ Seen FindFormula[]? $\endgroup$ – J. M.'s technical difficulties Nov 20 '15 at 15:45
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    $\begingroup$ You do not have to give the function for Mathematica to do the fit. What you are giving are called basis functions the combinations (linear or non-linear) of which form the fitted function. $\endgroup$ – Lotus Nov 20 '15 at 15:50
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    $\begingroup$ The curve you show looks easy to fit, but one needs to have data. Generally, I would play with several functions like x^a, where a<1 and may be x^a/(1+x^a) and alike. $\endgroup$ – Alexei Boulbitch Nov 20 '15 at 15:55
  • $\begingroup$ How do you define "best"? $\endgroup$ – chuy Nov 20 '15 at 16:50
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    $\begingroup$ @QuantumMechanics, please, take a look here as a starting point. And provide your data points. $\endgroup$ – garej Nov 20 '15 at 21:39

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