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### 4.2. More on Functions

In this section we will cover a few more ideas connected with functions that will be useful in later chapters.

#### 4.2.1. A Function as a Set of Point Pairs

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.

▪ Exploration:

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 Inches Stretched 1.2 2.4 3.5 4.9 6.1

Data such as this, resulting from observation or experiment, is called empirical data.

##### Figure 4.4. This may seem trivial, but the same method is used to measure the elasticity of a spring, a steel girder, or other structural member.

In technical work, we must often deal with pairs of numbers, rather than single values. If 10 pennies caused ...

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