My math professor in college explained functions to me like this:

 

We have a box with one opening where x can come in, and one exit, where y can come out. The box changes x into y. This is what we mean by y = f(x). For each value of x that goes in, a single value of y comes out, not several possible values.

 

When giving these type of concrete interpretations, we must not go overboard describing the concrete object so that they lose focus on the math. Keep repeating the math idea while explaining the image. E.g., with the above example of f(x), we do not need to go into great detail saying what type of machine it is. If we say it is a machine making computer cases out of steel, the focus becomes on the machine, rather than the math.

 

A function is not an equation.