Introduction to Relations and Functions

Introduction to Relations, Domain and Range

Please write down the following vocabulary words in your notebook. Fill in the definitions as you follow along with the presentation. You may also want to write down the examples of each.

RELATION -

DOMAIN -

RANGE -

Relation

*a set of ordered pairs

*We use braces { } to represent a set.

*{(2, 9), (4, -2), (7, 8), (1, -4)}

is an example of a relation because it is a {set} of ordered pairs.

A Relation can be represented in 3 different forms -

*As a table *As a mapping diagram *As a graph

WAYS TO REPRESENT A RELATION

DOMAIN

• the set of all X VALUES in a relation (set of ordered pairs

• the Independent Variable

• Input values

Ex. The domain of this relation

{(5,-2), (8,9), (2, -1), (-4, -2)}

is {5, 8, 2, -4}; all the x values

Notice we write the domain in braces { } because the numbers make up a set.

Multiple Choice

What is the domain of this relation? {(2,3), (-4,8), (-5,6)}

• {3, 6, 8}

• {2, -4, -5}

Multiple Choice

What is the domain?

• {1, 2, 3, 4, 5}

• (2, 3, 4, 5, 6}

Multiple Select

What is the domain?

• {0, 3, 6}

• {0, 1, 2}

If there are ever two of the same number in the relation, we only list the number ONCE.

Ex. {(2,3), (-1, -1), (2,7)}

The domain is {2,-1}; we only list the 2 ONCE.

Range

• the Y VALUES in a relation ( a set of ordered pairs)

• the Dependent Variable

• the Output Value

Ex. The range of this relation

{(5,-2), (8,9), (2, -1), (-4, -3)}

is {-2, 9, -1, -3}; all the y values

Notice we write the range in braces { } because the numbers make up a set.

Multiple Choice

What is the range of this relation? {(2,3), (-4,8), (-5,6)}

• {3, 6, 8}

• {2, -4, 5}

Multiple Choice

What is the range?

• {1, 2, 3, 4, 5}

• (2, 3, 4, 5, 6}

Multiple Select

What is the range?

• {0, 3, 6}

• {0, 1, 2}

If there are ever two of the same number, we only list the number ONCE.

Ex. {(2,3), (-1, 3), (2,7)}

The range is {3,7}: we only list the 3 ONCE.

Let's recap today's lesson: