Answer
See below.
Work Step by Step
A function is a rule that relates elements from a set A to elements of another set, B, in a way that EXACTLY one element of set B is assigned to EACH element of set A.
(for every input, there is a unique output).
The set A is called the set of inputs, or the DOMAIN of the function. If x is an element of the domain, we annotate its corresponding output with f(x).
The set R, containing all possible values of f(x)
is called the set of outputs or the RANGE of the function. R is a subset of B. (Not every element of B must be involved.)
A function can be defined with an equation, a table, a graph, or a verbal description. An arrow diagram is a diagram that shows which element of B is assigned to each element of A, by joining inputs with the corresponding outputs with arrows. (See below for an example.)
Example:
Let $A=\{B,C,E,G\}$ and $B$ = set of positive integers.
Define a function f, which allocates to each letter in set A, the ordinal number that the letter has in the English alphabet.
B is the second letter of the alphabet so f(B)=2,
C is the third, so f(C)=3.
f(E)=5, f(G)=7.
Above is a verbal definition of a function.
A tabular definition could be:
$\left[\begin{array}{lllll}
x: & B & C & E & G\\
f(x): & 2 & 3 & 5 & 7
\end{array}\right]$
A is the domain of f. $R=\{2,3,5,7\}$ is the range of f.
(R is is a subset of B.)
Below is an example of a line diagram defining the function.
