ppt.function.relations.powerpoint presentation

lesson ppt

1. Grade 8 – E. Hemingway Ms. Marjorie M. Estuita

2. Math Class Prayer Dear Lord , Thank you for the hundredfold blessings in our life. Help us to multiply love with one another. Divide our God given talent. May we add happiness and positive thoughts to everybody. And subtract wrongdoings and grudges in our hearts . This we ask in Jesus name…. Amen

3. Relations and functions Ms. Marjorie M. Estuita

4. Hello class…. Tell me with emoji you’re feeling today… Which emoji are you today??

5. Let’s have a recall… Determine the Quadrant or axis of the following points.

6. 1. M(3, -2) 7. x < 0 and y < 0 2. A(-4, -6) 8. x < 0 and y > 0 3. R(1, 2) 9. x > 0 and y > 0 4. J(-4, 3) 10. x > 0 and y < 0 5. D(0, 5 ) 6. Z(-3, 0) Q IV Q III Q I Q II y – axis x – axis Q III Q I Q II Q IV

7. Activity 1 Direction: Group the following into two different categories. Form some ordered pairs using the format: (item, platform)

8. Tiktok PTV 4 GMA 7 ABS CBN UNTV Instagram facebook twitter  

9. From the previous activity, let’s make a table according to its category. Social Media TV Network ( Tiktok , social media) (GMA 7, television network) ( facebook , social media) (UNTV, television network) (Instagram, social media) (PTV4, television network) (twitter, social media) (ABS CBN, television network) Guide Questions 1. How many items are there in each column? 2. How did you classify the two categories? 3. In the first category, enumerate all the first element in the ordered pairs? second element ? 4. In the second category, enumerate all the first element in the ordered pairs? S econd element? 5. From the ordered pairs you have formed in the two categories, is there a repetition in the first element? How about the second element? 6. Does the set of ordered pairs represent a relation?

10. relation A relation is any set of ordered pairs. The set of all the first coordinates is called the domain of the relation and the set of all the second coordinates is called the range . . 

11. function A function is a relation in which no two pairs in a set of ordered pairs have the same first element . NOTE: Every function is a relation, but some relations are not functions

12. Examples: a. {(1, 1), (2, 3), (3, 5), (4, 7), (5, 9)} domain (x): {1, 2, 3, 4, 5) range (y): {1, 3, 5, 7, 9) function b. {(3, -1), (0, 0), (-3, 0) (-6, 2)} domain (x): {3, 0, -3, -6} range (y): {-1, 0, 2} function c. {(2, 5), (2, 2), (2, −1), (2,0)} domain (x): {2} range (y): {5, 2, -1, 0} Not a function

13. Representations of Relations Aside from ordered pairs, a relation can be represented in four different ways: x 1 2 3 y 1 3 5 7 1. Table of values In the table, the domain is {0,1,2,3} and the range is {1,3,5,7}

14. 2. Mapping Diagram 1 is mapped to D, 2 to B, 3 to C and 4 to A

15. 3. Graph

16. 4. Rule Or Equation The value of y is 2 less than the value of x. In other words, this can be described by the equation y = x − 2.

17. Illustrative Example: Suppose Jimin is working in McDonalds near F. Torres High School and he earns ₱43 per hour. Questions: a. How much will Jimin earn if he works for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? P215 P172 P258 P301 P344

18. b. Is his earnings related to the number of hours of work? How? Jimin’s earnings can be represented by some other way like tables of value, graph, mapping diagram, equation or rule.

19. H represents the number of hours(x) while E represents his earnings (y) By Graph

20. By Mapping Diagram By Equation Or By Rule     Jimin’s earnings can be represented by E or y = 43x  

21. I. Determine if the given set of ordered pairs is a function or a mere relation and put a ✓ on the appropriate column. Ordered Pair Function Mere Relation 1. P = {(0,1), (1,2), (2,3)}     2. O = {0,2), (1,1), (3,7), (2,4)}     3. I = {(1,2), (2,4), (3,6), (4,8)}     4. N = {(4,1), (4,2), (4,3)}     5. T= {(0,0), (4,2), (9,3), (4, −2), (9, −3)}    

22.   II. Determine whether a given mapping diagram is a function or NOT a function. Not a function function function

23. Group Activity Suppose you are working in a coffee shop. You earn ₱48 per hour. Questions: a. How much will you earn if you work for 4 hours a day? 5 hours a day? 6 hours a day? 7 hours a day? 8 hours a day? b. Are your earnings related to the number of hours of work? How?

24. (The learners will be instructed to represent their answer in different ways.) Group 1 – by ordered pairs Group 4 – by graph Group 2 – by table Group 5 – by equation/rule Group 3 – by mapping diagram Questions to be used: a. How many elements are there in the set of ordered pairs you have made? b. What elements belong to the first set? second set? c. Is there a repetition of first coordinates? How about the second coordinates?

25. GENERALIZATION A __________ is any set of ordered pairs. The set of all the first coordinates is called the ________ of the relation and the set of all the second coordinates is called the _________ A _________ is a relation in which no two pairs in a set of ordered pairs have the same _____________. relation domain range function first element

26. Quiz State whether the given set of ordered pairs is a function or NOT. 1. (1, 2), (2, 3), (3, 4), (4, 5) 5. 2. (-1, 6), (-2, 7), (-3, 8), (-4, 9) 3. 4. x 1 1 2 y 2 8 3 7 x -3 -1 3 7 y 8 8 8 8 x 5 7 y 4 3 2 8

27. Answer key 1. function 2 . function 3. not 4. function 5. not

28. How well do you learn the lesson?