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Lesson 1 INTRODUCTION TO FUNCTIONS
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.
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Lesson 1 INTRODUCTION TO FUNCTIONS
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- 2. Learning Objectives: At theend 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 thecorrespondence of two sets. x y corresponds depends
- 9. INPUT - OUTPUT INPUT xy corresponds depends OUTPUT
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- 13. function Relation in whicheach element of the Domain is paired with exactly ONE element of the Range. x y corresponds ONE AND ONLY
- 14. ILLUSTRATION OF FUNCTIONS a.Setof Ordered Pair b.Mapping or Arrow Diagram c.Graphing
- 15. A. SET OFORDERED 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)}
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- 19. C. GRAPHING VERTICAL LINETEST (Pencil Test) If any vertical line passes through more than one point of the graph, then that relation is not a function.
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- 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
Editor's Notes
- #8 Imagine yourself that you were working in a gasoline station and you need to load two different engines. One is a truck and one is a car. Which engine would you load its tank firsts in order for them to finish almost at the same time.