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Suppose I have a set of several $(x,y)$ coordinates, how would I find some function $f(x)=y$ which satisfies these coordinates? Is there a website I can use? Does there always exist a function which satisfies any set of points?

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  • $\begingroup$ Are you talking about a set of $(x,y)$ coordinates? $\endgroup$
    – imranfat
    Aug 21, 2021 at 23:58
  • $\begingroup$ yes x , y coords $\endgroup$
    – physBa
    Aug 22, 2021 at 0:03
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    $\begingroup$ Given $n$ points you can find a unique $n-1$ degree polynomial that goes through them. Look up Lagrange interpolation. $\endgroup$ Aug 22, 2021 at 0:05

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If you have several points $(x,y)$ , then you can make a set $S$ as a collection of them. Now, if there exists no point $y,z$ and $y\neq z$ such that both $(x,y),(x,z)$ belongs to the set $S$, then according to definition of function, this set $S$ is a function and it has the property you want. Although it may not be possible to write this function with the help of $+,-,\times,\sin,\cos,\ln$ and variables. However, if you have a collection of points like this: $$S=\{(1,2),(1,3)\} $$

Then there exists no function with the property you want. That is : for any given collection of points there does not always exist a function with the property you mentioned.

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