Functions Defined By Data

The following table of values gives the daily closing price of a particular stock during the first two weeks of a particular month:

The first column shows the day of the month and the second column shows the corresponding closing price, in dollars. This information could have been collected from a morning newspaper or an online trading site. Each day, one new row could be added to the table.

The table is a function: It gives a rule for determining the unique closing price for any given day during the two-week period. Unfortunately, the rule only applies to past history. Is there a larger rule, extending into the future, of which the table shows only a part? Every stock trader would like to know!

What makes this table of values different from some other tables of values is that it was not generated by a known rule. It is merely a collection of data. We do not know what makes it go.