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October 26th, 2014, 11:51 AM   #1
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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?
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October 26th, 2014, 12:58 PM   #2
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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.
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Last edited by skeeter; October 26th, 2014 at 01:03 PM.
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October 26th, 2014, 01:00 PM   #3
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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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