
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 2,887 Thanks: 1506 
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.


Tags 
function, refer, term 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integral that cannot be written in term of elem function  Fanascom  Calculus  8  October 23rd, 2013 06:39 AM 
the 12 term of a G.P  kingkos  Algebra  2  December 21st, 2012 07:19 PM 
Refer me to a good Calculus 1 book  Hyperion  Math Books  6  September 24th, 2011 09:48 AM 
Refer me to a good Calculus 1 book  Hyperion  Calculus  6  September 11th, 2010 10:29 AM 
Term by term differentiation  forcesofodin  Real Analysis  4  August 14th, 2010 05:50 PM 