The document defines functions and relations. It reviews basic math operations and introduces the concepts of relations, inputs and outputs, domains and ranges. A relation is a correspondence between two sets, while a function is a special type of relation where each input has a single, unique output. Functions can be illustrated through sets of ordered pairs, mapping diagrams, and graphs where the vertical line test determines if a relation is a function. Students are given examples of relations and functions to identify which are functions.

1. FUNCTIONS
General Mathematics

2. Learning Objectives:
At the end of the session, students
should be able to:
1.define functions and relations;
2.relate the concepts of functions in real
life situations; and
3.participate in the class actively.

3. Review : Operations
• 5 + 9 =
• 2 + -8 =
• -14 + -7 =
• -2 + 18 =
14
-6
-21
16

4. Review : Operations
• 5 - 4 =
• 6 - 13 =
• -4 - 7 =
• 7 – (-5) =
1
-7
-11
12

5. Review : Operations
• (5) (7) =
• (9) (-6) =
• (-7) (12) =
• (-5) (-3) =
35
-54
-84
15

6. Review : Operations
• 20 / 5 =
• 15 / -5 =
• -16 / -2 =
• -30 / 6 =
4
-3
8
-5

8. RELATION
Refers to the correspondence of two sets.
x y
corresponds
depends

9. INPUT - OUTPUT
INPUT
x y
corresponds
depends
OUTPUT

10. RELATION
3
2
8
7
5
9
4
1
DOMAIN RANGE

11. RELATION
2
7
5
9
4
1

12. RELATION
3
2
8
7
9
4

13. function
Relation in which each element of the Domain is paired
with exactly ONE element of the Range.
x y
corresponds
ONE AND ONLY

14. ILLUSTRATION OF FUNCTIONS
a.Set of Ordered Pair
b.Mapping or Arrow Diagram
c.Graphing

15. A. SET OF ORDERED PAIR
1. {(3,2), (4,0), (5,1), (2,3)}
2. {(1,2), (0,3), (1,6), (5,4)}
3. {(3,4), (3,0), (3,1), (3,3)}
4. {(4,2), (3,2), (6,2), (5,2)}
5. {(5,3), (5,2), (3,2), (3,4)}

16. B. DIAGRAM
3
2
8
7
5
9
4
1

17. FUNCTION?
2
5
9
4
1

18. FUNCTION?
3
2
8
7
9
4

19. C. GRAPHING
VERTICAL LINE TEST
(Pencil Test)
If any vertical line passes through more
than one point of the graph, then that
relation is not a function.

20. C. GRAPHING

22. ACTIVITY
1.{(-3,1), (0,2), (2,4)}
2.{(1,5), (1,3), (4,5)}
3.{(5,6), (-3,0), (1,1), (-3,6)}
4.{(-2,1), (-1,-1), (0,1), (-1,1)}
5.y = 3x