A function is a rule connecting two sets such that for each
item in the first set there is just one item which it is related
to in the second set. The mathematical concept of a function
expresses dependence between two quantities, one of which
is given and the other produced. A function associates a single
output to each input element drawn from a fixed set, such
as the real numbers.
specify a function the input set (the domain) and the output
set (the range) should be stated. Usually they are sets of
numbers such as the real numbers. Functions can be represented
on number lines or by using the input and output numbers as
coordinates to obtain a graph. A function is often represented
by a letter.
example, the multiply by 7 function could be represented by
f. Then the function is written f: x -> 7x. which is read
as f is the function such that x goes to 7x.
The output corresponding to an input of x is written f(x)
(read as f of x).
For example, for the multiply by 7 function
f(x) = 7x.