Lesson 2: Relations: Summary

Math 10C Module 4

Module 4: General Relations

Lesson 2 Summary

In this lesson you investigated the following questions:

Why is it appropriate to connect the points on some graphs but not others?
How can you determine the limitations on the domain and range of a relation?

In this lesson you learned that a relation is a rule that relates one quantity to another. You learned that relations can be represented in several different ways, including a set of ordered pairs, a table, an arrow diagram, and a graph. Together with a partner, you also brainstormed other methods of representing relations.

You learned that where the values between graphed data points have meaning in the context of the question, the data is continuous and it is appropriate to join the points with a line or a smooth curve. By contrast, where the values between points have no meaning in the context of the question, the data is discrete and it is not appropriate to join the points.

In this lesson you also learned how to express the domain and range of discrete and continuous graphs. Just as there are several ways of representing relations, there are also many ways of expressing the domain and range of a relation. The restrictions on the domain and range can be stated using inequality symbols, or endpoints on a number line, and different styles of brackets. Another way to express domain and range is to restrict the number set to integers only.

To express the domain and range, you could use five different methods.

Method	Explanation
Words	The domain is all real numbers. The range is all real numbers greater than or equal to 0.
Number Line	This is the domain. This is the range.
Interval Notation	This is the domain: (−∞, ∞). This is the range: [0, ∞).
Set Notation	This is the domain: {x\| −∞ ≤ x ≤ ∞, x ε R} or {x\| x ε R}. This is the range: {y\| 0 ≤ y ≤ ∞, y ε R} or {y\| y ≥ 0, y ε R}.
List	This is continuous data, not discrete. So for this example, a list does not make sense as a way to express the domain and range.

In Lesson 3 you will study functions—a special type of relation. You will learn the difference between functions and non-functions. You will also discover a neat visual technique for identifying graphs that are functions!