Teacher: So what is the value of f(x) if x =3?
Student: Does f(x) mean f times x?
Teacher: No, no, no...f(x) is a function of x.
Student: Oh, it is a function of x?
Student: Oh, okay, I think I get it. So we can plug in a number for x and find out what f equals.
Teacher: Yeah, that's pretty close. Do you have another question?
Student: So, then is f like the slope of the line?
Teacher: *slaps forehead* Uncle!
Student: Well you said it is a function of x and of means to multiply.
Alright, so that didn't just happen in my class. But similar dialogues do take place right around the time I first introduce things like f(x) or sin(x). Kids always think that means that we are multiplying something by x. We usually end up discussing how often times functions need to have names like f(x) or g(x) so you can tell them apart. We don't spend too much time on function notation in middle school, but when it comes up, I would like a better way to explain it.
Don't act like that hasn't happened to you.
So how do you explain it?