The Never Ending Question

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?

Teacher: Right.

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?

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3 Responses to “The Never Ending Question”


  1. 1 Jessica April 24, 2009 at 3:32 pm

    In my algebra class (9th graders) we talk about f(x) and g(x) being nicknames for functions. You can say y = _____ or you can say f(x) = _____ (as long as the y = _____ is truly a function). It works the other way, too. That helps kids with the concept of graphing a function that is initially given to them as f(x).

  2. 2 Sarah April 24, 2009 at 5:18 pm

    I’m still trying to convince students 5x means 5 times x and not 5 plus x. (Don’t see too many 5 in front of the number that x is anymore at least.) It’s not what you need, but my quote recently is, “See how they’re right beside each other with no space in between? They’re too close; they’re making babies. And when you make babies you multiply.”

    I try to squeeze in sex ed when I can.

  3. 3 Nick April 24, 2009 at 5:44 pm

    I don’t know either…

    I’d go for the really straight forward approach with that.

    do y = 2x + 3 with x and y axes.
    then do f(x) = 2x + 3 with x and f(x) axes.
    explain that y = 2x + 3 and f(x) = 2x + 3 are interchangeable.

    f(what?) = 2(what?) + 3

    Tell them about the SAT-ish problems with strange function notation

    &&x&& = 3x – 5, so &&2&& = …

    my .02


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