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If a grocery store sells apples priced at 12 cents each, they may wish to make a list of the cost of various quantities of apples. For example:
You can, of course, extend this list as far as necessary.
Notice that to find the cost of any quantity of apples you may use the formula
C = .12 - N
If you substitute a numeral for 'N', you can find the corresponding cost by using this formula.
For example, to find the cost of 17 apples you substitute '17' for 'N':
C = .12 - 17
If you multiply .12 by 17, you find that the cost of 17 apples is $2.04.
We can assume that the grocery store is not interested in knowing the cost of fractional parts of an apple.
Thus the values of 'N' are simply the whole numbers
0, 1, 2, 3, . . .
and the values of 'C' are simply the multiples of .12.
It is also useful to consider the set of ordered pairs:
(0,0), (1, .12), (2, .24), . . .
The first member of an ordered pair is called the first component, and the second member of an ordered pair is called the second component. For example, the first component of the ordered pair (3, .36) is 3, and its second component is .36. Notice that in the set of ordered pairs which you are considering, no two ordered pairs have the same first component. For example, the two ordered pairs (1, .12) and (2, .24) have different first components.
A set of ordered pairs that satisfies the condition that no two ordered pairs in the set have the same first component is called a function. Thus, the set of ordered pairs given above is a function.
The set of ordered pairs given above may be described as the set of all ordered pairs (n, c), where the first component is a whole number, such that
c = n - .12
The domain of a function is the set of first components of the set of ordered pairs of which the function consists. The range of a function is the set of second components. In the example considered above, the domain of the function is the set of whole numbers, and the range of the function is the set of multiples of .12.
Instead of listing the costs of various quantities of apples, the dealer may make a graph:
The dot that is above '1' and to the right of '.12' illustrates the point that corresponds to the ordered
pair (1, .12). The dot that is above '2' and to the right of '.24' illustrates the point corresponding to the
ordered pair (2, .24). By referring to the graph, the dealer can see at a glance that the cost of 4 apples is 48 cents.
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