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October 26th, 2014, 11:51 AM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  What does the term 'function' refer to?
What exactly is a function when people talk about it. If $\displaystyle f(x) = 2x$, is the function f, f(x), 2x, or is the function the equation f(x) = 2x? I am confused about this, because I have seen it described in many ways. Also, when people say y is a function of x, what exactly does that mean? Is y the function, or is y = f(x) the function?

October 26th, 2014, 12:58 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 
a function is known by many symbols ... y is a function f(x) is a function u and v are variables often used to represent functions ... there are more. The key thing is, a function value (or output of the function) depends on the input value of one (or more, possibly) other value(s). per your example ... f(x) = 2x , f(x) and 2x both represent the value of a function for some given value of x. It also could be written y = 2x ... same/same. f(3) = 2(3) = 6 , f(w+1) = 2(w+1) , f() = 2() f(3) and 6 are the (same) function value when the independent variable, x, is 3 f(w+1) and 2(w+1) are the (same) function value when the independent variable x is (w+1) f() and 2() are the (same) function value when the independent variable x is I might also mention that each input value to a function yields only one output value. hope this gives you a start ... do a web search if you want a more complete explanation. Last edited by skeeter; October 26th, 2014 at 01:03 PM. 
October 26th, 2014, 01:00 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
The function is the map between x and 2x. Often it's written f(x), but with the understanding that x here is a formal variable rather than some unknown at which the function is evaluated.


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