### 5-2 Relations

```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 #57
Graph the following points. Then state what
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.
2.
3.
4.
Set of ordered pairs
Table
Graph
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
x
y
1
1
3
2
3
2
2
3
2
3
1
4
1
4
3
Table
Mapping
Guided Practice #57
Represent the following relation as a table, a
mapping, and a graph: { (2, 3) , (2, -1) , ( 4, -1 ),
(3, 3) }
x
y
X
Y
?
?
Guided Practice
Represent the relation from Drill #61 as a mapping:
x
-3
-1
1
1
3
4
y
3
2
1
3
-2
-2
X
-3
-1
1
3
4
Y
3
2
1
-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)}
x
y
x
y
swap x and y

1
4
4
1
-3
2
2
-3
7
-9
-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 table
1. Swap the x and y values
Inverse
x
y
x
y
-1.5
3
3
-1.5
1
4
4
1
-1
4
2
5
-1.5
6
4
-1
5
2
6
-1.5
2. Write as a set of
ordered pairs:
{(3,-1.5),(4,1),(-1,4),
(-1,4),(2,5),(-1.5,6)}
Classwork
Complete 5-2 Study Guide Worksheet
Homework complete section 5-2 (unit outline)
Read Section 5-3 Equations as Relations
```