Math 10C Module 4: Lesson 3

Module 4: General Relations

 

Lesson 3 Summary

In this lesson you investigated the following questions:

  • Why is it that some relations are not functions?

  • How can you tell if a relation is a function?

In this lesson you learned that a function is a special type of relation. Each input value of a function has only one output value. The important idea is not that the output value is unique, but that there is only one output value. Some relations conform to this rule and are called functions. Other relations can only be described as relations, not functions. You studied an example relating four sons and their mother. Since each son only has one mother, the son-mother relationship is analogous to a function. On the other hand, since the mother has four sons, the mother-son relationship is not analogous to a function, since the input (mother) has more than one output (four sons). Despite this, all functions are considered relations since they can be expressed as a set of ordered pairs.

Besides learning the difference between a relation and a function, you also learned how to tell if relations, expressed in a variety of ways, are functions. You developed personal strategies for identifying functions and non-functions. The vertical line test is an example of such a strategy for testing relations expressed as graphs. If the vertical line intersects the graph in more than one point at a time, then the graph fails the test and is not a function.

In the remaining lessons in this module you will investigate the slope of a line. You will learn how to use the slope to interpret the rate of change of one variable compared to another variable. You will also learn how to use slope to predict values on graphs.