# Relations and functions

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### Relations and functions

1. 1. Relations And Functions
2. 2. Observe the following sets. {(2,4),(5,0),(9,8),(-1,5),(-13,-4),…} {(-2,-4),(-1,-2),(0,0),(1,2),(2,4),…} {(3,2),(2,1),(1,0),(0,-1),(1,2),…} x -2 2 -2 2 y 3 4 5 6
3. 3. A relation is a set of ordered pairs. {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} This is a relation The domain is the set of all x values in the relation {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} The range is the set of all y values in the relation {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} domain = {-1,0,2,4,9} These are the x values written in a set from smallest to largest range = {-6,-2,3,5,9} These are the y values written in a set from smallest to largest
4. 4. Domain (set of all x’s) Range (set of all y’s) 1 2 3 4 5 2 10 8 6 4 A relation assigns the x’s with y’s This relation can be written {(1,6), (2,2), (3,4), (4,8), (5,10)}
5. 5. First Set: Domain( Fourth Year students) Second Set: Range(set of positive integers) Correspondence: Each student’s age Maricel Aiza Marc Joseph 16 17 12
6. 6. One- to - many One- to - one many –to - one Types of Relations
7. 7. SPOT THE DIFFERENCE One- to - many FUNCTIONS One- to - one many –to - one NOT a FUNCTION/S
8. 8. Anne Curtis Sam Pinto Christine Hermosa Iya Villania Gorgeous Anne Curtis Sam Pinto Christine Hermosa Iya Villania Sam Milby Oyo Boy Sotto Drew Arellano Richard Guttierez FUNCTIONS Correspondence: Celebrities’ characteristic Correspondence: Celebrity Couple
9. 9. Anne Curtis Sam Pinto Christine Hermosa Iya Villania Gorgeous NOT FUNCTIONS
10. 10. A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. Set A is the domain 1 2 3 4 5 Set B is the range 2 10 8 6 4 A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. Must use all the x’s A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. The x value can only be assigned to one y This is a function ---it meets our conditions All x’s are assigned No x has more than one y assigned
11. 11. A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example show on the previous screen had each student getting the same grade. That’s okay. 1 2 3 4 5 2 10 8 6 4 Is the relation shown above a function? NO 2 was assigned both 4 and 10 A good example that you can “relate” to is students in our math class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example shown on the previous screen had each student getting the same grade. That’s okay.
12. 12. Determine whether the given relation is a function or not. {(2,4),(5,0),(9,8),(-1,5),(-13,-4),…} {(-2,-4),(-1,-2),(0,0),(1,2),(2,4),…} {(3,2),(2,1),(1,0),(0,-1),(1,2),…} x -2 2 -2 2 y 3 4 5 6
13. 13. GRAPHS Function Not FunctionVertical Line Test ONE POINT TWO/ MORE POINTS
14. 14. Skill Booster A. Identify if the given set is a function or not. 1. Place Tourist Spots Albay Chocolate Hills Bohol Fort Santiago Banaue Tiwi Hot Spring Ilocos Norte Banaue Rice Terraces Baguio Malacaήang of the North Manila Luneta Park Mayon Volcano Camp John Hay
15. 15. 1. Student Grade in Math Ana 85 Joey Joy 89 Ezra Avin 90 Skill Booster A. Identify if the given set is a function or not.
16. 16. 1. Player Sports Nepomuceno Basketball Pacquiao Fencing Jaworski Boxing Gomez Bowling Skill Booster A. Identify if the given set is a function or not.
17. 17. 4. {( 1,2), (1,4),(3,2),(3,5)} 5. {(5,2),(4,1),(3,0), (4,2) 6. {(-1,-1),(0,0),(1,-1),(2,2)} 7. 8. Skill Booster A. Identify if the given set is a function or not. X 0 -1 1 -2 Y 1 2 2 4 X -2 0 4 5 Y -1 1 5 6
18. 18. Skill Booster B. Which graph shows a function? Why?
19. 19. 1. The range is 2 less than the domain. 1. Twice the domain is the range. 3. The range is 3 more than twice the domain. Skill Booster C. Construct a table of values for the following conditions. x y x y x y
20. 20. Seatwork: A. Determine whether the relation is a function or not. 1. Domain: Students Correspondence: Birthdate Range: Days of the year 2. Domain: people in the city Correspondence: color of the eyes Range: set of colors 1. Domain: Students Correspondence: grade in Science Range: positive integers
21. 21. 4. Domain: set of integers Correspondence: Square root of the number Range: Set of real numbers 5. Domain: Set of integers Correspondence: double each number Range: set of integers Challenging Tasks: A. Determine whether the relation is a function or not.
22. 22. B. 1. What is the greatest number of x- intercepts that a function may have ? y – intercepts? Explain your answer. 2. Is ( x + 2 ) 2 + ( y – 3) 2 = 9 a function? Explain your answer.