Question

People learn new languages for many different reasons—from personal enrichment to school credit to necessity. When approaching a new language, we find patterns that are the product of rules. For example, languages have rules that govern grammatical structures, pronunciations, and word order. Communication is difficult when we break those rules. Compare learning about functions to learning a new language. How are they similar?

Answer 1

I'd like to offer the alternative perspective. I think that learning grammar rules through a written account of the system (text books) is something that is only useful to a language learner under the following conditions:
they have already learned how to have a conversation in the language 
they are naturally curious now about how the patterns in how it fits together 
they would like to learn how to read in the language
they would like to improve their accuracy for a specific purpose (eg professional or educational)

Answer 2

Learning mathematical functions is a lot similar to learning a new language. 

Like in learning a new language, its very important to work out on the relationship between words & their uses. In the same way, in functions, it is very important to understand the relationship between variables. 

Firstly, a strong foundation should be built in understanding algebra. Algebra is a key to understand functions. Just like its very important to form the base foundation of syllables & basic grammar in the language.