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Algebra 1 Ch2.3 Function & Formulas

Question from Jake:

We have a question on functions and the fact that they don’t always have a formula. Would this be an example of a function without a formula? Say, for example that there was a function for rain, and the function was almost completely random, 2 inches one month, 4 inches the next, 10 inches the following, and 1 inch the last month measured. This graph is completely random. The amount of rain could be based on dozens of variables, i.e. rain patterns, amount of moisture in the air, etc. A graph like this could also go for stocks, storms, etc. Would these all be examples of functions with no formula?

Thanks a lot

Answer from Dr. Callahan:

Yes – what you have described in your examples are what we call random functions – since we often MODEL these relationships based on random processes. Fact is, they are NOT random – but the massive amount of data needed to build a formula makes it not worth the trouble.
But either way – they are functions that do not have formulas.