Functions in calculus... I never understood them until I learned about functions in programming several years later. They're the same damn thing! I really wish I had learned to program before learning calculus.
When we learned about functions back in something like 5th grade, I noticed that my classmates were very confused by the concept. I also remembered that I found the explanations in the book and the ones from our teacher quite unclear.
My guess back then was that the notation was partly to blame for that -- and I still think that's true.
So, my questions to you are:
1) were you taught the "f(x) = 3x + 2"-style notation? 2) have you seen the "x --> 3x+2"-style before? Or the "f: x --> 3x+2"-style, where we give the function the name f? 3) did you find it confusing that f(x) was sometimes used to refer to the function and sometimes to its value when applied to x? The notation of question 2 should eliminate that confusion.
I'm guessing that part of the confusion was also that your teachers were unclear on what functions could be used for -- but didn't they ask you to draw graphs for various functions? And didn't they also introduce functions like sin/cos/tan?