1. 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.

2. Drill #57
Graph 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 )

3. Biology
Page 262.
There are 1.4 million classified species of microorganisms, invertebrates, plants, fish, …

4. 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

5. 4 ways to represent relations
Set of ordered pairs
Table
Graph
Mapping

6. (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 4

7. 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

8. Guided Practice Represent the relation from Drill #61 as a mapping:
X Y
-3 3
-1 2
1 1 4 x y -3 3 -1 2 1 -2 4

9. (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.

10. 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 y x y 1 4 -3 2 7 -9 x y 4 1 2 -3 -9 7

11. Find the Inverse
Write the inverse of the following relation as a set of ordered pairs: x y
-1.5 3 1 4 -1 5 2 6

12. First make a table 1. 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)}
Inverse x y 3
-1.5 4 1 -1 2 5 6 x y
-1.5 3 1 4 -1 5 2 6

13. Classwork Complete 5-2 Study Guide Worksheet
Homework complete section 5-2 (unit outline)
Read Section 5-3 Equations as Relations