5-2 Relations

Objective: To identify the domain, range, and inverse of a function and to show relations as sets of ordered pairs, tables, mappings, and graphs.

Drill #57Graph the following points. Then state what

quadrant they are in:

1. A ( 4, 5 ) 2. B ( -3, 2 )

3. C ( -1.5, - 4 ) 4. D ( 0, -5 )

5. E ( -5, 0 ) 6. F ( 3.5, -2.5 )

Biology

Page 262.

There are 1.4 million classified species of microorganisms, invertebrates, plants, fish, …

Relations **Relations are a set of ordered pairs.

(10.) Domain: The set of all the x- coordinates of a relation

(11.) Range: The set of all the y- coordinates of a relation

4 ways to represent relations

1. Set of ordered pairs

2. Table

3. Graph

4. Mapping

(12.) Mapping **Definition: A mapping pairs each element in the domain

with an element in the range.

Example: { (1,4), (2, 2), (3, 1), (4, 3) }

X Y

1

2 3

3 2

4 1

Table Mapping

x y

1 3

2 2

3 1

4 3

Guided Practice #57Represent the following relation as a table, a

mapping, and a graph: { (2, 3) , (2, -1) , ( 4, -1 ), (3, 3) }

X Y

? ?

x y

Guided PracticeRepresent the relation from Drill #61 as a mapping:

X Y

-3 3

-1 2

1 1

3 -2

4

x y

-3 3

-1 2

1 1

1 3

3 -2

4 -2

(13.) Inverse

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

To find the inverse of a relation for each ordered pair swap x and y values.

Inverse

The inverse of a relation can be obtained by switching the coordinates in each ordered pair.

Example:

Relation: Inverse:

{(1,4),(-3,2),(7,-9)} {(4,1),(2,-3),(-9,7)}

swap x and yx y

1 4

-3 2

7 -9

x y

4 1

2 -3

-9 7

Find the Inverse

Write the inverse of the following relation as a set of ordered pairs:

x y

-1.5 3

1 4

4 -1

5 2

6 -1.5

First make a table1. Swap the x and y values

2. Write as a set of ordered pairs:

{(3,-1.5),(4,1),(-1,4),

(-1,4),(2,5),(-1.5,6)}

x y

-1.5 3

1 4

4 -1

5 2

6 -1.5

Inverse

x y

3 -1.5

4 1

-1 4

2 5

-1.5 6

ClassworkComplete 5-2 Study Guide Worksheet

Homework complete section 5-2 (unit outline)

Read Section 5-3 Equations as Relations