GENERAL MATHEMATICS-FUNCTION_LESSON1.pptx

FIRST LESSON ON FUNCTION - GENERAL MATHEMATICS

1. Function

2. Objectives The learner represents real life situations using functions, including piece wise functions . evaluates a function

3. PROBLEM A supermarket holds a closing-out sale. All merchandise are sold 30% discount. For the convenience of the shoppers, the marketing supervisor considers a table of mark prices ($x) and their corresponding selling prices ($y). A portion of the table is given and he/she needs your help to complete it.

4. PROBLEM 30% of Php 50.00 = Php 15 PhP 50.00 – PhP 15.00 = PhP 35.00 Marked Price ( PhP x) 50 100 150 200 250 300 350 Selling Price ( PhP y) 35 70 105 140 175 210 245

5. The set of ordered pairs of marked price and selling price : (50, 35) , (100, 70), (150, 105), (200, 140) , (250, 175), (300, 210) ,(350, 245) There is exactly one value of y that corresponds to every value of x. And that’s what we called FUNCTION

6. Functions VS Relations Relations – any set of ordered pairs Functions - A type of relation where there is exactly one output (RANGE) for every input (DOMAIN).

7. Domain and Range Domain – (set of inputs) it is the first coordinates Range – (set of outputs) it is the second coordinates

8. Example Pairing of names and their height RELATIONS: ( names, height) or (height, names)

9. Example NAME HEIGHT James 6’8 Irving 6’3 Love 6’10 Thompson 6’9 Smith 6’7 Clarkson 6’5 FUNCTION ( james , 6’8) , ( irving , 6’3), (love, 6’10), ( thompson , 6’9), (smith, 6’7), ( clarkson , 6’5)

10. FUNCTION - For every x there is exactly one y A= { (1,2) , (2,3) , (3,4) , (4,5) } X 1 2 3 4 Y 2 3 4 5 ONE TO ONE RELATION IT IS A FUNCTION

11. FUNCTION - For every x there is exactly one y A= { (1,2) , (2,2) , (3,2) , (4,5) } X 1 2 3 4 Y 2 3 4 5 MANY TO ONE RELATION IT IS A FUNCTION

12. FUNCTION - For every x there is exactly one y A= { (2,2) , (2,3) , (2,4) , (4,5) } X 1 2 3 4 Y 2 3 4 5 ONE TO MANY RELATION IT IS NOT A FUNCTION

13. FUNCTION B= { (1,0) , (0,1) , (-1,0) , (0,-1) } X 1 -1 Y 1 -1 MANY TO MANY RELATION IT IS NOT A FUNCTION

14. GRAPH of a Function Vertical line test A graph of a mathematical relation is a function if any vertical line drawn passing through the graph intersects the graph at exactly one point.

15. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function

16. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function

17. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function

18. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function Function

19. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function Function Not a Function Function Not a Function Not a Function

20. Real life situation The area A of a circle is a function of its radius r . A =   Set of input Function rule Set of output Areas of Circle All radii (r) A = All areas (A) Set of input Function rule Set of output Areas of Circle All radii (r) All areas (A)

21. Real life situation The table below shows the PHILPOST rates for sending printed materials Weight Price 20 g and below Php 14 More than 20 g but not over 50 g Php 32 More than 50 g but not over 100 g Php 54 More than 100 g but not over 250 g Php 132 More than 250 g but not over 500 g Php 263 More than 500 g but not over 1000 g Php 525

22. Real life situation The table below shows the PHILPOST rates for sending printed materials Set of input Function Rule Set of output Postal price Weight of material to be sent {Php 14 Php 32, PhP 54, PhP 132, Php 263, Php 525 Set of input Function Rule Set of output Postal price Weight of material to be sent

23. DOMAIN AND RANGE OF A FUNCTION The area A of a circle is a function of its radius r . A =