Lesson 1 INTRODUCTION TO FUNCTIONS

General Mathematics

1. FUNCTIONS General Mathematics

2. Learning Objectives: At the end of the session, students should be able to: define functions and relations; relate the concepts of functions in real life situations; and 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 - 8 4 15

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

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

8. INPUT - OUTPUT INPUT x y corresponds depends OUTPUT

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

10. RELATION 2 7 5 9 4 1

11. RELATION 3 2 8 7 9 4

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

13. ILLUSTRATION OF FUNCTIONS Set of Ordered Pair Mapping or Arrow Diagram Graphing

14. 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)}

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

16. FUNCTION? 2 5 9 4 1

17. FUNCTION? 3 2 8 7 9 4

18. 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.

19. C. GRAPHING

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