How does one express a function of a single variable and a constant?

  1. How would someone go about writing a general expression for a function of a single variable and a constant? For example, if we have a function of two variables 'x' and 'y' we can use f(x,y). If we had a function of 'x' and the constant '∏' is it acceptable to write it as f(x,π)?
     
  2. jcsd
  3. Curious3141

    Curious3141 2,970
    Homework Helper

    Why would you want to do that? By definition, a constant does not change, so it should not influence the dependent variable. Functions like ##x \rightarrow \pi x## or ##x \rightarrow \sin \pi x## are completely adequately represented as ##f(x)## (omitting the ##\pi##).
     
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  4. This is in reference to new functions where the constant, π for this particular example, is relevant. Proper notation is paramount otherwise there is no point.

    On that note, and considering the confusion about the example f(x,∏), this particular representation does not seem appropriate, do you have an alternative suggestion?
     
    Last edited: Aug 18, 2014
  5. There are lots of notations for a function ##f## in variable ##x## with some constant parameter ##a##, besides just plain old ##f(x, a).## Some other examples are ##f_a(x)##, ##f^{(a)}(x)##, ##f(x; a).##
     
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  6. Excellent, thank you olivermsun. Do any of those have a particular meaning or is,
    ##f(x, a)## = ##f_a(x)## = ##f^{(a)}(x)## = ##f(x; a).## for all cases?

    Does anyone else have anything to add?
     
    Last edited: Aug 18, 2014
  7. It depends on the context it's used in. Use a notation that doesn't cause confusion in your context and be consistent.
     
  8. HallsofIvy

    HallsofIvy 40,804
    Staff Emeritus
    Science Advisor

    I have seen the notation f(x; c) used to indicate a function of the variable x which depends upon the parameter c. I think the word "parameter" is better here than "constant".

    (You understand that the distinction between a "variable" and a "constant" that can take on different values is pretty slim!
    f(x; c) is understood to mean a family of functions of x, each possible value of c giving a different function in that family.)
     
  9. I have seen many examples of 'family of functions' (some even posted on PF) so this notation is good to know.

    On another note, for this particular instance I am interested in notation for a function of one variable that also happens to have a single known constant (e.g. π, or e, or phi, etc.) as part of that function. If I had a function of a single variable 'x' and constant '∏' is f(x,∏) an acceptable form to describe said function?
     
  10. If it's just a constant like e then just don't put it.
     
  11. Only if there's no chance of confusion.

    For example, I think writing ##\log_e(x)## and ##\log_{10}(x)## is a good idea when either or both could be used.
     
  12. I understand this sentiment, however if it were that simple I wouldn't be here. Do you think using the form f(x,some constant) is adequate?
     
  13. It seems adequate. I've seen it in textbooks and published papers alike.
     
  14. Very good, thank you (again).
     
  15. In this case you would write f(x) = lnx =log_e x. You're still not writing the e in the name of the function, f.

    I prefer ## f_c(x) ## to indicate that the function is only a function of x.
     
  16. You are. The ##e## appears in the subscript of the function name ##\log##. Anyway it's just one possible convention. The point is to distinguish between base ##e## and ##10## clearly.
     
  17. Hm, yeah I suppose you're right about this one. Though a comment, even here you aren't using the notation ##f(x,a)##, it's still the notation ##f_a(x)##.
     
    Last edited: Aug 20, 2014
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