What is the name of a function that has no equation

Question

I've heard that the amount of snowfall is a function of date. This makes sense to me as there is only one specific date, so therefore the date does not produce two different outputs.
But if you were to plot the amount of snowfall and the date you wouldnt be able to find a relationship between the days. So is it possible to have a function where you don't know the relationship and if so what is it called?

Answer 1

There is no specific name for such a function.  It is simply an unknown function.  However, if you have a plot of snowfall vs. date, some kind of curve will be traced, and you can use computational methods to try to fit an equation to the data.  The fitted equation will be the mathematical function. The function may be named after the individual who first succeeds in performing the data fit and publishing the results in a reputable science journal.

Answer 2

While all functions are relations, since they pair information, not all relations are functions.