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Mathematics 8 relations and functions.pptx
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- 2. Let’s pray... Dear God, Maywe, through your blessings, add purity to the world, subtract evil from our lives, multiply Your good news, and divide Your gifts and share them with others. Amen.
- 3. Read it aloud.. Mathematics isfull of fun, with so much to learn Profits are added, while losses are subtracted Degrees are multiplied, and percentage is divided Geometry is full of mystery, Algebra has a big history Integers as different as brothers, Lines as parallel, Angles are similar, Math is necessary in life, Without it,it is difficult to survive.
- 4. Attendance Say “present”, whenyour name is called.. Say present!
- 5. House Rules: F U N C T I O N – focus on the activity - use the materials appropriately – no cheating – cooperate with your group – time management – insist everyone to share their ideas – observe silence – negotiate with your group
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- 7. Review time... 1. A representationof a point in the form of (x,y) Graph Table Domain Ordered Pair
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- 9. GREAT JOB! Proceed tothe next question :)
- 10. Review time... 2.Any set ofordered pairs. Relation Domain Range Function
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- 12. GREAT JOB! Proceed tothe next question :)
- 13. Review time... 3. The setof first coordinates of the ordered pairs. Graph Domain Range Function
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- 15. GREAT JOB! Proceed tothe next question :)
- 16. Review time... 4. The setof second coordinates of the ordered pairs. Graph Domain Range Function
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- 18. GREAT JOB! Proceed tothe next question :)
- 19. Review time... 5. What typeof representation is being used? Graph Table Rule Mapping Diagram
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- 21. GREAT JOB! Proceed tothe next question :)
- 22. Review time... 6. What typeof representation is being used? Graph Table Rule Mapping Diagram
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- 24. GREAT JOB! Proceed tothe next question :)
- 25. Review time... 7. What typeof representation is being used? Graph Table Rule Mapping Diagram
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- 27. GREAT JOB! Proceed tothe next question :)
- 28. Review time... What type ofrepresentation of relation is being used? Graph Table Rule Mapping Diagram
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- 30. GREAT JOB! Proceed tothe next question :)
- 31. Let’s have thetitle of our topic….
- 32. OBJECTIVE/S: Relations and Functions Atthe end of the session, the students will be able to: VERIFIES IF A GIVEN RELATION IS A FUNCTION. M8AL-IIc-2 DEVELOP COOPERATION AND ENHANCE SPEED IN DOING A TASK.
- 33. Lets have an activity... “Classifyyour Relation”
- 34. Identify each typeof relations given. You have three minutes to answer. ● One –to – One Correspondence ● One – to – Many Correspondence ● Many – to – One Correspondence ● Many – To – Many Correspondence
- 35. ● One –to– One Correspondence ● One – to – Many Correspondence ● Many – to – One Correspondence ● Many – To – Many Correspondence
- 36. Answer the following: ●What can you observe in the given relation? ● Can you determine the domain and the range? ● What type of correspondence is the given relation? ● How did you classify each type of relation or what is your basis in determining the type of relation?
- 37. re·la·tion /rə lāSH(ə)n/ ˈ Learn topronounce noun the way in which two or more concepts, objects, or people are connected; a thing's effect on or relevance to another. "Similar: connection relationship association Link correlation
- 38. Relation Any set ofordered pairs (x,y). Ex. (2,3) The set of first coordinates is called the domain of the relation. The set of all second coordinates is called the range of the relations.
- 39. Relation Any set ofordered pairs (x,y). Ex. (2,3) The set of first coordinates is called the domain of the relation. The set of all second coordinates is called the range of the relations. Domain Range Ordered pairs (1,5) (2,6) (3,7)
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- 44. Task 3. “Am Irelated?”
- 45. Each group willbe tasked to give an example of each type of correspondence. You can use examples that you can relate/ experience in their daily lives (name and age, address, religion, gender, favourite food or colour, the food they had for breakfast/ lunch, and the like). Questions: 1. Among the types of correspondence which are functions? 2. Does one – to – one correspondence between elements always guarantee a function? How about many – to – one or many- to many? Justify your answer. 3. Does one – to – many correspondence between elements always guarantee a function? Justify your answer.
- 46. 2 5 8 6 K TO 10CRITICAL CONTENT IN MATHEMATICS 8 RELATION FUNCTION ? A B C D SET A SET B SITUATION A A B C D E 1 2 3 5 SET A SET B SITUATION B
- 47. What is afunction? ● Function - is a special type of relation. It is a relation in which every element in the domain is mapped to exactly one element in the range. ● Thus, a set of ordered pairs (relation) is a function if no two distinct ordered pairs have two equal abscissas or x-coordinate.
- 48. RELATION 2 5 8 6 FUNCTION RELATION FUNCTION ? A B C D SET ASET B SITUATION A A B C D E 1 2 3 5 SET A SET B SITUATION B
- 49. FUNCTION RELATION MAPPING DIAGRAM HOWTO DETERMINE WHETHER A RELATION IS A FUNCTION OR NOT
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- 51. No element of“x” should be repeated ORDERED PAIR (x,y) HOW TO DETERMINE WHETHER A RELATION IS A FUNCTION OR NOT A. (1,2), (3,4), (5,6), (7,8) = B. (1,2), (1,4), (1,6), (1,8) = C. (1,2), (2,2), (3,2), (4,2) = D. (1,2), (5,4), (5,6), (7,8) = Function Relation Function Relation
- 52. THE VERTICAL LINETEST. If the vertical line touches the graph no more than once, the graph represents a function. It is a FUNCTION.
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- 54. It is aFUNCTION. TEACHER SUBJECT Sir Reyes Science Sir Biñas English Maam Noronha English Maam Buladaco Mathematics TABLE
- 55. FUNCTION X Y 1 6 27 3 8 4 9 5 10 TABLE X 1 1 0 -1 2 Y -2 -3 0 1 1 RELATION No element of “x” should be the same.
- 56. Remember: All functions arerelations, but some relations are not function.
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- 59. It is NOTa FUNCTION. HOTS Question: Analyze before you answer.
- 60. It is NOTa FUNCTION. 2 3 4 5 6 20 21 22 23 24 25 x y
- 61. Lets have an activity... “ArrangeYour Relation”
- 62. Directions: Match upthe correct table, graph, map and ordered pairs together and determine if the relation is a function or not a function.
- 63. CRITERIA 10 1215 TOTAL DELIVERY The presentation was not well executed The presentation was good The presentation was well- executed CLARITY AND LOUDNESS Students’ voice was not clear Some of the students’ voice can be clearly heard All of the students’ voice can be clearly heard TIMELINESS Students did not finish the task on time Students finished the task just on time Students finished the task before the time limit GROUP PARTICIPATION Most group members did not participate Some of the group members did not participate All of the group members participated and worked well together
- 64. Write the letterof your answer on spaces where they belong on the table. Table 1 Table 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
- 65. Write the letterof your answer on spaces where they belong on the table. Table 1 Table 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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- 67. 2 3 4 56 7 8 9 10 11 12 13 14 15 16
- 68. 3 4 5 6 78 9 10 11 12 13 14 15 16
- 69. 4 5 6 78 9 10 11 12 13 14 15 16
- 70. 7 8 9 1011 12 13 14 15 16
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- 73. Let’s answer these questions.. 1. Howdid you determine the arrangement of your table? 2. What is the domain and the range of each ordered pairs? 3. What is your basis in connecting the domain and the range of each set of ordered pairs?
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- 79. Let’s analyze... ● Amongthe set of ordered pairs, which one are functions? ● What type of representation are the functions? ● How did you determine the functions and not functions among the given ordered pairs?
- 80. What have youlearned today? > What is a function? ● is a special type of relation. It is a relation in which every element in the domain is mapped to exactly one element in the range. > How do we verify if given relation is a function? ● If each input lead to only one output. X ● There are different ways to verify if a given relation is a function. ● Ordered Pair, Mapping Diagram, Table
- 81. Quiz Write your answeron your activity notebook.
- 82. Verify if thegiven relation is a function. Write FUNCTION if it is a function and RELATION if it is not a function. 1. {(8,3), (7,5),(6,5),(5,4),(4,4)}
- 83. 2. Verify if thegiven relation is a function. Write FUNCTION if it is a function and RELATION if it is not a function.
- 84. 3. Verify if thegiven relation is a function. Write FUNCTION if it is a function and RELATION if it is not a function.
- 85. 4. Verify if thegiven relation is a function. Write FUNCTION if it is a function and RELATION if it is not a function.
- 86. 5. Verify if thegiven relation is a function. Write FUNCTION if it is a function and RELATION if it is not a function.
- 87. 1. Function 2. Relation 3.Function 4. Function 5. Relation LET’s CHECK!
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- 89. Assignmen t Read in advanceabout the range and domain of a function and function notation.
- 90. Beth Aslee L.Buladaco Have a Good day! Thank you for listening
Editor's Notes
- #1 Good morning class, welcome to our Mathematics 8 class, and im your teacher for today Maam Beth, So to start our class let’s have our prayer to be led by Hernan..
- #2 OK Hernan pls turn on your microphone.. In Jesus Name we pray Amen. Thank you Hernan.
- #3 so for our math poem reading, I believe it is Wella’s turn.. So wella please read our math poem for today… Ok Thank you Wella. A virtual clap for wella.. Ok thank you. Class please continue practicing on reading..Dont stop reading.
- #4 So for our attendance please say present if your name is called..ok? Hernan Binas, Ricson Reyes, and Robwela Noronha.. Im glad you are all present this morning.. So how are you feeling today? Nakain na ba kayo? I Hope so...
- #6 Ok Lets have our review of our past lesson, about the basic concept of relations.. And the different types of relations. You can raise your hand if you want to answer. Example (x,y) = (3,2)
- #7 Ok Lets have our review of our past lesson, about the basic concept of relations.. And the different types of relations. You can raise your hand if you want to answer. Example (x,y) = (3,2)
- #10 Relation
- #32 Ok so for our objectives this morning may I call on Ricson to please read.. Ok Thank you ricson So take note of our goal this morning, that at end of our class, you will be able to verify if a given relation is a function. And also to with our activities this morning, our target is to develop cooperation and enhance speed in doing task.. So ready na ba kayo?
- #33 OK lets have an activity! We call this arrange your relation..
- #37 When we say relation it means, it something related to, has a connection, Any two more concept, object, people, something has a common connection, reason with each other for example : your relation to mother, or brother or father, Another example is your hernan, what is your relation to wella? You are classmates. In mathematics, It is also in the related meaning.. But more specifically, it talks about ordered pairs.
- #38 Ordered pairs - it is a pair…ex in graphing a point in a cartesian plane.. Point (2,3).. It means that the point is located in the coordinate x =2, and y= 3. Also when we talk of ordered pairs, it has two sets..pair xa diba? set A or set B. Example here, in set A, we have 1,2,3 and in set B, we have 5,6,7. 1 is related to 5, 2 to 6 and 3 to 7. That is what we call a relation. And our ordered pairs are (1,5) , (2,6) (3,7)
- #39 Ordered pairs - it is a pair…ex in graphing a point in a cartesian plane.. Point (2,3).. It means that the point is located in the coordinate x =2, and y= 3. Also when we talk of ordered pairs, it has two sets..pair xa diba? set A or set B. Example here, in set A, we have 1,2,3 and in set B, we have 5,6,7. 1 is related to 5, 2 to 6 and 3 to 7. That is what we call a relation. And our ordered pairs are (1,5) , (2,6) (3,7)
- #40 Example here, in set A, we have 1,2,3 and in set B, we have 5,6,7. 1 is related to 5, 2 to 6 and 3 to 7. That is what we call a relation. And we also have different types of relations, one -one, one to many, many to one, many to many. And we are going to look at it later kung saan jan ang function or hindi function. So what do think is this type of relation? Is it a function or not?? Ok we will answer that later..
- #44 OK lets have an activity! We call this arrange your relation..
- #46 I have here a situation A and B, what type of relation is Situation A? How about B? A - one-one relation and B - many-to-many relation. So i have a question? Situation A - is it a function or not/? How about b? What is your answer? Why? So to verify, let first discuss what is a function..
- #47 So let us discuss first what is a function.. So, in a function, you have to remember this, all x should only have one y. So a relation is a function if lahat ng x isa lamang ang y. So pwede ang isang y ang my maraming x, pero di pwedeng ang x ang maraming y.
- #48 So let us check… Situation A - ang x ba natin maraming y? Yes or no? No, so therefore it is a function Situation B - ang x ba natin maraming y, or naulit ung x natin? Yes, to therefore it is not a function, it is a relation but not a function.
- #49 So the question is how are we going to determine if a relation is function or not? Since we have different representation of relations, we have different ways to know if that relation is a function.. we are going to discuss it one by one. In this example, the first one is a function and the other one is not,, why? Again, no element of “x” should be the same or repeated. So as you can see on the first example, there is a one-one relation, so it means that every x or the domain is relate to one range or to our y.. So therefore, it is a function. On the other example, the one to many, x is relate to many y, 1 -2 & 3 and 5 to 5&6. Kaya, it is anot a function. Therefore it is only a relation..
- #50 Again, it is a function, kasi ung x hindi naulit.. In no. 4 it is a relation, kasi naulit ang x.
- #51 Ok this time naman is ordered pair,, a,b,c,and d, which one do you think is a function or nt a function? You answer first… a. Who answered function? B? C ? d?
- #52 This time, we have a graph.. As you can see there, the red graph is our relation.. To test if is it a function or not, we are going to do the vertical line test. (REad vertical line test) the yellow is our vertical line, so we are goint to run the test.. Passing a vertical line on a graph, and if that line passes only one point/spot at a time, then it is a function. As you can see, no two points were touched at the same time.. So it mean that it is a function.
- #53 Next is the graph, on the first example, our graph there is the circle, yan ung relation, ung line na nagcross, that is our x-y coordinate. We are going to do the vertical line test.. If it touches two points or more then it is not a function.
- #56 Ibig sabihin, pag sinabi nating function, it means na relation yan xa, but if it is a relation, we need to verify first if it is a function.. So we have learned today, different ways to determine if a function is a relation.
- #57 OK lets have an activity! We will have a quiz bee...
- #58 OK lets have an activity! We will have a quiz bee... Analyze
- #59 It is not a function.. Why it is not a function?
- #60 It is not a function.. Why it is not a function? Because the problem says x is the factor of y.. When we say factor what does it mean? a number that divides another number evenly—i.e., with no remainder. Ex what is are the numbers that could divide 12? 3, 6 and 2, and 1.. Therefore 2, 3, 6 and 12 are the factors of 12.. So in the given what numbers are divisible by 2? 3? 4?...6
- #61 OK lets have an activity! We call this arrange your relation..
- #62 We have here a chart and it has 4 questions.. So do you still remember your lesson about the different representations of relation.. So what you are going to do is… (read direction) Column 1 - is table, 2- graph 3- mapping diagram 4 - ordered pairs and 5 - you are going to answer if it is a function or not a function...
- #64 We have here numbered blank spaces, from 1-16, so you from table 2, you are going to fill up the table 1.. If we are doing this face to face, we r goig to cut out the boxes, but since online tayo, den ganito nlng gawin natin.. We have there Number 1-16 in table 1, and then just write the letter of your answer from table 2.for example number 1, if u think that the answer is letter a from table 2, then you write in number 1, letter A... Did you understand class, So are you ready? Do you have questions? I will give you 5 minutes to do this task. Kaya ba? Ok kaya…
- #65 Ok you can start now, observe our timer.. Can you see it clearly? Ok are you done, if you are done just say your done in the chatbox.. Ok if you are done, lets check ur answer...
- #66 We have here a chart and it has 4 questions.. So do you still remember your lesson about the different representations of relation.. So what you are going to do is… (read direction) Column 1 - is table, 2- graph 3- mapping diagram 4 - ordered pairs and 5 - you are going to answer if it is a function or not a function...
- #67 Ok so what is the answer for box 1,
- #72 ( read after next slide) How did you determine the arrangement of your table? The first column is the table, the second column is the graph column, the 3rd, is the mapping diagram and the 4th is the ordered pairs.. We need to match if the representation belongs to the group.. What is the domain and the range of each ordered pairs? So, in order to check if it placed in the correct row, we need to look at the domain and the range.. The first row, the domain are the x - coordinates ( -5,-3, 0, 3). The range are the y - coordinates (1,2,3,4) How about number 2? No. 3? no.4? What is your basis in connecting the domain and the range of each set of ordered pairs? We based it on the given ordered pairs, the first number is the x - coordinate, and the 2nd number is the y - coordinate.
- #73 Ok so before we proceed in answering whether the relation is a function, lets answer first on these questions? How did you determine the arrangement of your table? The first column is the table, the second column is the graph column, the 3rd, is the mapping diagram and the 4th is the ordered pairs.. We need to match if the representation belongs to the group.. What is the domain and the range of each ordered pairs? The first row, the domain are the x - coordinates ( -5,-3, 0, 3). The range are the y - coordinates (1,2,3,4) How about number 2? No. 3? no.4? What is your basis in connecting the domain and the range of each set of ordered pairs? We based it on the given ordered pairs, the first number is the x - coordinate, and the 2nd number is the y - coordinate.
- #74 How did you determine the arrangement of your table? The first column is the table, the second column is the graph column, the 3rd, is the mapping diagram and the 4th is the ordered pairs.. We need to match if the representation belongs to the group.. What is the domain and the range of each ordered pairs? So, in order to check if it placed in the correct row, we need to look at the domain and the range.. The first row, the domain are the x - coordinates ( -5,-3, 0, 3). The range are the y - coordinates (1,2,3,4) How about number 2? No. 3? no.4? What is your basis in connecting the domain and the range of each set of ordered pairs? We based it on the given ordered pairs, the first number is the x - coordinate, and the 2nd number is the y - coordinate.
- #78 What can you observe in the graphs? Or the table? Or the Mapping Diagram? Or ordered pairs? In question no 1 and 2? The x coordinate, it is repeated or not? No, the x coordinate or the domain, or the input is not repeated. How bout in question 3? Is it repeated or not? Yes, the y coordinate, the range or the output, is repeated. Example in question 3, there are two -2., in question 4, there are four -3.
- #79 OK so let’s proceed.. Let’s analyze.. Do you have any idea?
- #80 It is not a function.. Why it is not a function? Because the problem says x is the factor of y.. When we say factor what does it mean? a number that divides another number evenly—i.e., with no remainder. Ex what is are the numbers that could divide 12? 3, 6 and 2, and 1.. Therefore 2, 3, 6 and 12 are the factors of 12.. So in the given what numbers are divisible by 2? 3? 4?...6
- #88 Ok what do you mean by this? There are lot of things that could scratch our relationship with others, our actions, our words, sometimes joke lng sa atin, pero it could hurts others feeling.. Minsan u do not know, dinadala na pala ng frend mo or nung classmate mo, workmate mo, or colleague mo for a long time. ung mga words that hurted them.. So let us be careful in handling the feelings of others. Or sometimes, best thing to really ask for forgiveness or have a one on one talk with that person.. You will be given a chart,
- #89 Good morning class, welcome to our Mathematics 8 class, and im your teacher for today Maam Beth, So to start our class let’s have our prayer to be led by Hernan..