# How do I find a function with specific coordinates?

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?

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

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: $$S=\{(1,2),(1,3)\}$$