ObjectiveThe student will be able to:

1. graph ordered pairs on a coordinate plane.

2. identify the domain and range of a relation.

3. show relations as sets and mappings.

In the beginning of the year, I created a seating chart for my classes. I created 5 rows of desks with 4 desks in each row. Brian sits in the third row at the second desk (3,2) and Dwanda sits in the second row at the third

desk (2,3). Are these seats the same?

No!! The seats (3,2) and (2,3) are called ordered pairs because the order in which

the pair of numbers is written is important!!

Who is sitting in desk (4,2)?

A B C D E

F G H I J

K

P

L M N O

Q R S T

4

3

2

11 2 3 4 5

N

Ordered pairs are used to locate points in a coordinate plane.

x-axis (horizontal axis)

origin (0,0)

y-axis (vertical axis)5

5

-5

-5

In an ordered pair, the first number is the x-coordinate. The second number

is the y-coordinate. Graph. (-3, 2)

•

5

5

-5

-5

What is the ordered pair for A?

1. (3, 1)

2. (1, 3)

3. (-3, 1)

4. (3, -1)

5

5

-5

-5

• A

What is the ordered pair for B?

5

5

-5

-5

• B

1. (3, 2)

2. (-2, 3)

3. (-3, -2)

4. (3, -2)

What is the ordered pair for C?

1. (0, -4)

2. (-4, 0)

3. (0, 4)

4. (4, 0)

5

5

-5

-5

• C

What is the ordered pair for D?

5

5

-5

-5

• D

1. (-1, -6)

2. (-6, -1)

3. (-6, 1)

4. (6, -1)

Write the ordered pairs that name points A, B, C, and D.

A = (1, 3)

B = (3, -2)

C = (0, -4)

D = (-6, -1)

5

5

-5

-5

• A

• B• C

• D

The x-axis and y-axis separate the coordinate plane into four regions, called quadrants.

II

(-, +)

I

(+, +)

IV

(+, -)

III

(-, -)

Name the quadrant in which each point is located

(-5, 4)

1. I2. II3. III4. IV5. None – x-axis6. None – y-axis

Name the quadrant in which each point is located

(-2, -7)

1. I2. II3. III4. IV5. None – x-axis6. None – y-axis

Name the quadrant in which each point is located

(0, 3)

1. I2. II3. III4. IV5. None – x-axis6. None – y-axis

How about some more definitions? The domain is the

set of 1st coordinates of the ordered pairs.

The range is the

set of 2nd coordinates of the ordered pairs.

A relation is a

set of ordered pairs.

Given the relation {(3,2), (1,6), (-2,0)},

find the domain and range.

Domain = {3, 1, -2}

Range = {2, 6, 0}

What would this be?

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

A bad relationship!! Ha! Ha!

The relation {(2,1), (-1,3), (0,4)} can be shown by

1) a table.

2) a mapping.

3) a graph.

x y2-10

134

2-10

134

Given the following table, show the relation, domain, range, and mapping.

x -1 0 4 7y 3 6 -1 3

Relation = {(-1,3), (0,6), (4,-1), (7,3)}

Domain = {-1, 0, 4, 7}

Range = {3, 6, -1, 3}

Mappingx -1 0 4 7y 3 6 -1 3

You do not need to write 3 twice in the range!

-1047

36-1

What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)}

1. {2, 3, 4, 4}

2. {1, 2, 3, 1}

3. {2, 3, 4}

4. {1, 2, 3}

5. {1, 2, 3, 4}

Answer Now

What is the range of the relation{(2,1), (4,2), (3,3), (4,1)}

1. {2, 3, 4, 4}

2. {1, 2, 3, 1}

3. {2, 3, 4}

4. {1, 2, 3}

5. {1, 2, 3, 4}

Answer Now

Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x).

Write the relation and the inverse.

Relation = {(-1,-6), (3,-4), (3,2), (4,2)}

Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}

-134

-6-42

Write the inverse of the mapping.

-3

43-12

1. {(4,-3),(2,-3),(3,-3),(-1,-3)}

2. {(-3,4),(-3,3),(-3,-1),(-3,2)}

3. {-3}

4. {-1, 2, 3, 4} Answer Now