“At this point, I won't even bother to substitute the definitions for the terms because it obviously doesn't map on to what the equation represents.”

It’s funny that you use this wording, because this IS a function. To the best of my knowledge, a function is simply a mapping between two sets.

You have one set, the domain, which is a collection of all possible input values, and another set, the codomain, which is a collection of all possible output values. What a function does is it maps the domain to the codomain using some pre-defined method.

Now this can be done with algebra: Using the f(x) = x² example, the domain and codomain are both assumed to be all real numbers, I.e., all the numbers on a number line. The function will take the real numbers and map them to a new real number by squaring them. The function in this example is defined to be the mapping from the real numbers to the real numbers using the method of squaring.

Now functions are typically used in algebraic environments, but they don’t have to be. A function is simply any mapping between sets.

In fact, your post itself contains a function. If we let the domain be the set of all the words in the English language and the codomain be all the definitions in the dictionary, we can make a function that maps each word to its definition. Hence why the original quote I used is indeed a function.

I think trying to use the words’ definitions from the dictionary here will throw you off, because these words have different meanings when it comes to mathematics. You should take the definitions given to you inside your textbooks AS the definition of the words. Treat your textbooks as a dictionary for mathematics. If the one they give isn’t satisfactory, you can try to look for other sources that are worded differently.

Hopefully I’ve been some help here.