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The Concept of Relation

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Lesson Focus

The Concept of Relation

Algebra Foundations

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You will define relations, the domain (input) and range (output) of a relation, and represent a relation by listing ordered pairs, mapping, and graphing.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Define a relation.
  • Identify the domain (input) and range (output) of a relation.
  • Represent a relation by listing ordered pairs, mapping, and graphing.

Everything You'll Have Covered

Relation terminology explained

A relation is actually a relationship between two sets. The first set is called the domain and is often referred to as the input. The second set is called the range and is often referred to as the output.

Relation defined

A relation happens when some elements in the domain (input) are paired with one or more elements from the range (output).

Expressing relations

Relations are expressed in a variety of ways. A relation can be expressed in a mapping diagram (see the diagram below left). The domain (input) is on the left side and the range (output) is on the right side.

Relations can be expressed by graphing (see the diagram below middle). The ordered pairs created from either the mapping diagram or set of ordered pairs can be graphed as individual ordered pairs on a coordinate plane.

Finally, relations are also expressed by listing (see the diagram below right). The input value and output value can be written together to form an ordered pair. Each ordered pair represents one element in the relation.

Note that a relation can be expressed in all of these. They can also be quickly translated from one expression to the next.

The following key vocabulary terms will be used throughout this Activity Object:

domain - the set of input values for which a relation is defined

element - each object in a set; also called a member

input - the elements that define the domain set

mapping diagram - a visual representation of a relation such that some input values are paired with at least one output value

ordered pairs - a pair of numbers used to locate a point on a coordinate plane. An ordered pair is written in the form (x, y) where x is the x-coordinate and y is the y-coordinate

output - the elements that define the range set

range - the set of all output values produced by a relation

relation - a relationship between two sets of information where some value of the first variable is paired with one or more values of the second variable

set - a group of entities with one or more common characteristics; entities can be referred to as members, elements, or objects

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should know the definitions of ordered pair, input, output, domain, and range.
Course Algebra Foundations
Type of Tutorial Concept Development
Key Vocabulary domain, input, mapping