1.6 - Relations

Relation

Relation – a set of ordered pairs

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Ways to Represent Relations:

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Ways to Represent Relations: as a set

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Ways to Represent Relations: as a set

in a table

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Ways to Represent Relations: as a set

in a table

on a graph

Relation – a set of ordered pairs

(relationship btw. 2 numbers!)

Ways to Represent Relations: as a set

in a table

on a graph

in a mapping

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table x y

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table x y

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table x y

-1

0

-3

-2

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table x y

-1

0

-3

-2

Relation – a set of ordered pairs(relationship btw. 2 numbers!)

Ways to Represent Relations: as a setin a tableon a graphin a mapping

Example 1(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

1. a table x y

-1 2

0 -3

-3 2

-2 -2

2. a graph

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

2. a graphGraph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

3. a mapping

3. a mapping

X Y

3. a mapping

X Y

-3

-2

-1

0

3. a mapping

X Y

-3 -3

-2 -2

-1 2

0

3. a mapping {(-1,2),(0,-3),(-3,2),(-2,-2)}

X Y

-3 -3

-2 -2

-1 2

0

3. a mapping {(-1,2),(0,-3),(-3,2),(-2,-2)}

X Y

-3 -3

-2 -2

-1 2

0

3. a mapping {(-1,2),(0,-3),(-3,2),(-2,-2)}

X Y

-3 -3

-2 -2

-1 2

0

3. a mapping {(-1,2),(0,-3),(-3,2),(-2,-2)}

X Y

-3 -3

-2 -2

-1 2

0

3. a mapping {(-1,2),(0,-3),(-3,2),(-2,-2)}

X Y

-3 -3

-2 -2

-1 2

0

Inverse Relation

Inverse Relation - switch the x and y values in each ordered pair!

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range:

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range:

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

Inverse:

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

Inverse: {(-4,2)

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

Inverse: {(-4,2),(-4,3)

x y

2 -4

3 -4

5 -7

6 -8

Inverse Relation - switch the x and y values in each ordered pair!

Example 2

Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.

{(2,-4),(3,-4),(5,-7),(6,-8)}

Domain: {2, 3, 5, 6}

Range: {-8, -7, -4}

Inverse: {(-4,2),(-4,3),(-7,5)(-8,6)}

x y

2 -4

3 -4

5 -7

6 -8