Lesson-1_Representation-of-Functions-Functions-as-Model.pdf

GENERAL MATHEMATICS Romano L. Gabito, LPT  UNIVERSITY PRAYER Lord God of all wisdom We pray for the La Consolacion University Philippines that she may be faithful to the purposes of our foundresses, Mother Rita and Venerable Mother Consuelo. Continue to...

GENERAL MATHEMATICS Romano L. Gabito, LPT  UNIVERSITY PRAYER Lord God of all wisdom We pray for the La Consolacion University Philippines that she may be faithful to the purposes of our foundresses, Mother Rita and Venerable Mother Consuelo. Continue to promote the search for truth and knowledge and be an inspiration for others to follow. May we be a community of scholars sharing this ambition, caring for one another and loyal to the truth revealed to us as your disciples. AMEN. WELCOME BACK TO SCHOOL STUDENTS! REPRESENTATION OF A FUNCTION  LEARNING OBJECTIVES define function and its key components of a function: input, process, and output; apply functional concepts to real-world scenarios; and develop a positive outlook towards mathematical problem-solving.  REPRESENTATION OF A FUNCTION GRAPHS TABLE OF MAPPING VALUES RELATION  RELATION A set of ordered pairs. An ordered pair is a set of numbers written in a particular order. SET OF VALUES EXAMPLE FIRST SECOND DOMAIN RANGE (x , y) Relation: {(I, 1), (L,2), (0,3), (V,4), (E,5), (M,6), (A, 7), (T,8), (H,9)}  RELATION MORE EXAMPLES S = {(1, 3), (2, 4), (-1, 0)} Domain: {1, 2, -1} Range: {3, 4, 0} D = {(A, H), (B, I), (C, J), (D, K), (E, L)} Domain: {A, B, C, D, E} Range: {H, I, J, K, L} TYPES OF RELATION  TYPES OF RELATION ONE-TO-ONE RELATION Each element of the domain corresponds with exactly one element of the range. Domain: {2, 4, 6} Range: {3, 6, 9} Relation: {(2, 3), (4, 6), (6, 9)}  TYPES OF RELATION ONE-TO-MANY RELATION Each element of the domain corresponds with two or more elements of the range. Domain: {2, 4, 6} Range: {3, 6, 9, 12, 15} Relation: {(2, 3), (2, 6), (4, 9), (6, 12), (6, 15)}  TYPES OF RELATION MANY-TO-ONE RELATION Two or more elements of the domain correspond with one element of the range. Domain: {2, 4, 6, 8, 10} Range: {3, 6, 9} Relation: {(2, 3), (4, 3), (6, 6), (8, 9), (10, 9)}  TYPES OF RELATION MANY-TO-MANY RELATION Two or more elements of the domain correspond with one element of the range. Domain: {2, 4, 6, 8, 10} Range: {A, B, C, D, E} Relation: {(2, B), (2, D), (4, E), (6, A), (6, C), (8, D), (10, C)} let’s try! TYPES OF RELATION ONE TO MANY TYPES OF RELATION MANY TO ONE TYPES OF RELATION ONE TO ONE TYPES OF RELATION MANY TO MANY FUNCTION  FUNCTION is a relation in which each element of the domain corresponds to exactly one element of the range. FIRST SET OF SECOND COORDINATES INPUT OUTPUT (x , y)  FUNCTION FUNCTION IS LIKE A MACHINE INPUT PROCESS OUTPUT  FUNCTION it is a set of relations that have a unique value of the dependent variable (or the range) in every value of independent variable (or the domain). FUNCTION OR NOT FUNCTION FUNCTION OR NOT FUNCTION FUNCTION FUNCTION OR NOT FUNCTION NOT FUNCTION FUNCTION OR NOT FUNCTION FUNCTION FUNCTION OR NOT FUNCTION NOT FUNCTION VERTICAL LINE TEST  VERTICAL LINE TEST A graph is a function if and only if no vertical line intersects the graph in more than one point. EXAMPLES FUNCTION NOT FUNCTION  FUNCTIONS AS REPRESENTATION OF REAL-LIFE SITUATION  MATHEMATICAL MODELLING It is a process by which you start with a real-life situation and arrive at a quantitative solution using the tools of mathematics.  MATHEMATICAL MODELLING "You are planning your birthday party and want to give each guest a souvenir of chocolate candies. If each souvenir costs 500 ₱100, create a number 1000 sentence that shows how to 2000 calculate the total cost for buying souvenirs for all your guests." MATHEMATICAL MODELLING  MATHEMATICAL MODELLING STEP 1 Given  MATHEMATICAL MODELLING STEP 2 Simplify STEP 3 Find the area function ANY QUESTIONS OR CLARIFICATIONS?  QUESTION 2. How do functions impact your daily life? 3. Explain how functions are used in real-world applications? Provide an example.  LET’S PRACTICE DETERMINE THE OUTPUT: MATHEMATICAL MODEL 1. 4. A smartphone battery's life is influenced by various factors, including screen brightness, usage of apps, and network connectivity. Let's model battery PASS OR FAIL: VERTICAL LINE TEST life as a function of screen brightness. 2. 3. What is the expected battery life at 50% screen brightness?  LET’S PRACTICE DETERMINE THE OUTPUT: 1. PASS OR FAIL: VERTICAL LINE TEST 2. 3. FAILED PASSED  LET’S PRACTICE MATHEMATICAL MODEL STEP 4: Substitute Step 3 to b (y-int) STEP 1: Let y = battery life 3 = 80m + 6 - 20m m = screen brightness 3 = 60m + 6 3 - 6 = 60m 6 = 20m + b -3 60= 60m 60 3 = 80m + b m = -0.05 STEP 2: Formula: Linear Equation STEP 5: Substitute m to equation b y = mx + b b = 6 - 20(-0.05) STEP 3: Substitute b=6+1 b=7 STEP 6: Simplify 6 = 20m + b y = (-0.05)(50) + 7 b = 6 - 20m y = 4.5 hours  DO YOU UNDERSTAND THE TOPIC FOR TODAY?  LEARNING OBJECTIVES define function and its key components of a function: input, process, and output; apply functional concepts to real-world scenarios; and develop a positive outlook towards mathematical problem-solving.  CLOSING PRAYER Dear Lord, Thank you for this productive and interactive time together. Thank you for your wisdom and guidance. Thank you for the opportunity to learn from one another and grow closer in our faith.  CLOSING PRAYER We ask that the word of God will continue to be planted in our hearts and minds as we go about our days. We ask God to bless each one of us and our families, friends, neighbors, classmates, teachers, and everyone else who has been touched by this class. Bless us with your peace, love, joy, and hope as we go forward in faith. AMEN.