9 2 relations
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9.2 Relations. CORD Math Mrs. Spitz Fall 2006. Objectives. Identify the domain, range and inverse of a relation, and Show relations as sets of ordered pairs and mappings. Assignment. Pgs 361-363 #4-41. Definition of the Domain and Range of a Relation.

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9.2 Relations

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9 2 relations

9.2 Relations

CORD Math

Mrs. Spitz

Fall 2006


Objectives

Objectives

  • Identify the domain, range and inverse of a relation, and

  • Show relations as sets of ordered pairs and mappings


Assignment

Assignment

  • Pgs 361-363 #4-41


Definition of the domain and range of a relation

Definition of the Domain and Range of a Relation

  • The domain of a relation is the set of all first coordinates from the ordered pairs. The range of the relation is the set of all second coordinates from the ordered pairs.


Table mapping graph what s the difference

Table/Mapping/Graph – What’s the difference?

  • A relation can also be shown using a table, mapping or a graph. A mapping illustrates how each element of the domain is paired with an element in the range. For example, the relation {(2, 2), (-2, 3),(0, -1)} can be shown in each of the following ways.

x

y

2

-2

0

2

3

-1


9 2 relations

Ex. 1: Express the relation shown in the table below as a set of ordered pairs. Then determine the domain and range.

Ordered Pairs:

(0, 5), (2, 3), (1, -4), (-3, 3), and (-1, -2)

Domain (all x values):

{0, 2, 1, -3, -1}

Range (all y values):

{5, 3, -4, 3, -2}


9 2 relations

Ex. 2: Express the relation shown in the graph below as a set of ordered pairs. Then determine the domain and range. Then show the relation using a mapping.

Ordered Pairs:

(-4, -2), (-2, 1), (0, 2), (1, -3), and (3, 1)

Domain (all x values):

{-4, -2, 0, 1, 3}

Range (all y values):

{-2, 1, 2, -3, 1}


9 2 relations

Ex. 2: Express the relation shown in the graph below as a set of ordered pairs. Then determine the domain and range. Then show the relation using a mapping.

Ordered Pairs:

(-4, -2), (-2, 1), (0, 2), (1, -3), and (3, 1)

-4

-2

0

1

3

-2

2

-3

1

Domain (all x values):

{-4, -2, 0, 1, 3}

Range (all y values):

{-2, 1, 2, -3}

In this relation, 3 maps to 1, 0 maps to 2, -2 maps to 1, -4 maps to -2 and 1 maps to -3.


Inverse of relation

Inverse of relation

  • The inverse of any relation is obtained by switching the coordinates in each ordered pair of the relation. Thus the inverse of the relation {(2, 2), (-2, 3), (0, -1)} is the relation {(2, 2), (3, -2), (-1, 0)}. Notice that the domain of the relation becomes the range of the inverse and the range of the relation becomes the domain of the inverse.


Definition of the inverse of a relation

Definition of the Inverse of a Relation

  • Relation Q is the inverse of relation S if an only if for every ordered pair, (a, b) in S, there is an ordered pair (b, a) in Q.


9 2 relations

Ex. 3: Express the relation shown in the mapping below as a set of ordered pairs. Write the inverse of this relation. Then determine the domain and range of the inverse.

Ordered Pairs:

(0, 4), (1, 5), (2, 6) and (3, 6)

0

1

2

3

4

5

6

Inverse of the relation:

(4, 0), (5, 1), (6, 2) and (6, 3)

Domain of inverse (all x values):

{4, 5, 6}

Range of inverse (all y values):

{0, 1, 2, 3}

In this relation, 3 maps to 1, 0 maps to 2, -2 maps to 1, -4 maps to -2 and 1 maps to -3.


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