How to define a function by the values ​​of the pairs y;x?

Question

Mathematics

Is it possible to somehow mathematically determine what kind of function (linear, logarithmic, etc.) if there are any known pairs (let's say more than two) of its values ​​y; x?

Answer 1

For example, as implemented here: https://planetcalc.ru/5992/
Just keep in mind that many data sets can be equally well (or equally badly) described by functions of different types at the same time.

Answer 2

In my opinion, it is easier to set up a neural network. You will not even have to look for the names of your function basis, it will simply give you a numerical answer.

Answer 3

Most likely there will be many answers.
If the accumulation of points is similar to "horns" on a plane, then the cosine, parabola and hyperbolic cosine are equally suitable for the function.
And here it is very important to understand that there will be no clear answer.