1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Many ways to give a function

  1. May 23, 2009 #1
    "There are many ways to give a function: by a formula, by a plot or graph, by an algorithm that computes it, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (see, for example, inverse function). In applied disciplines, functions are frequently specified by their tables of values or by a formula. Not all types of description can be given for every possible function, and one must make a firm distinction between the function itself and multiple ways of presenting or visualizing it."

    This is a quote from: http://en.wikipedia.org/wiki/Function_(mathematics [Broken])

    in the last sentence he mentions "one must make a firm distinction between the function itself and multiple ways of presenting or visualizing it."

    I`m now confused because when I think of a function I think of one of its representations e.g. formulas; the author says that I should make a distinction between the ways of presenting/visualizing and the function itself.. how do I do so? and when the word "function" is mentioned how should I interpret it in my mind?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 23, 2009 #2
    Re: Functions

    Well you can think of a function any way you want really as long as you understand what it's defined to be. A f function is a set of ordered pairs such that if f(x) = y and f(x) = y' (or (x,y) and (x,y') are members of the set) then y = y'. It's useful to think about it as a curve in a plane or a set of ordered pairs or to look at an equation that can be used to find the values of the function depending on the context. I think that the Wikipedia page wanted to make the point that not all functions can be represented in each form; so if a function is defined in an way which you are unfamiliar with, and not as an equation or graph, then that doesn't mean that the function isn't defined properly or isn't a genuine function etc.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook