In this section we will cover a few more ideas connected with functions that will be useful in later chapters.
We have said that a function or relation can be given in forms other than an equation, such as a set of point pairs, a verbal statement, or a graph. Here we will have another look at sets of point pairs and verbal statements, and do graphing in the next chapter.
Try this. Suppose you want to describe how "strong" or how "weak" a certain rubber band is. Hang the band from a shelf, as in Fig. 4-4, tape a ruler alongside, and use a paper clip to attach a plastic bag. Put some pennies into the bag and record the change in length of the band. Then change the number of pennies and record the length. Repeat for different numbers of pennies.
When finished, how did you report your findings? You probably expressed your results not as single numbers, but as pairs of numbers, something like the following.
|Number of Pennies||10||20||30||40||50|
Data such as this, resulting from observation or experiment, is called empirical data.
In technical work, we must often deal with pairs of numbers, rather than single values. If 10 pennies caused ...