Lecture-1_Relations-Functions (1).pdf

PABLO ROMAN NATIONAL HIGH SCHOOL SENIOR HIGH SCHOOL DEPARTMENT General Mathematics LECTURE # 1 RELATIONS & FUNCTIONS OBJE...

PABLO ROMAN NATIONAL HIGH SCHOOL SENIOR HIGH SCHOOL DEPARTMENT General Mathematics LECTURE # 1 RELATIONS & FUNCTIONS OBJECTIVES: Define relation, domain and range. Determine the domain and range of a relation. Define function. Determine whether the given is a function or not. ❖ RELATIONS = It is a set of ordered pairs (x, y). Example: A = {(1, 3), (2, 5), (3, 9), (4, 11), (1, − 15)} Ordered pairs can also be called coordinates, or point. ABSCISSA – is the first element of ordered pairs. ORDINATE – is the second element of an ordered pair. ❖ DOMAIN The domain is the set of all x values in a relation. 𝐷𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑆𝑒𝑡 𝐴 = {1, 2, 3,4} ❖ RANGE The range is the set of all y values in a relation. 𝑅𝑎𝑛𝑔𝑒 𝑜𝑓 𝑆𝑒𝑡 𝐴 = {3, 5, 9,11, −15} ACTIVITY #1 Determine the domain and range of the following relations. 1. 𝐴 = {(−3, −4), (−2,5), (−1,5), (0,6)} 2. 𝐵 = {(−2, 5), (0,5), (2, 5), (4, 5)} 3. 𝐶 = {(0,3), (0,6), (−2, −4), (−4, −5)} 4. 𝐷 = {(1,0) ( 0,1), (−1,0), (0, −1)} 5. 𝐷 = {(−4, 2) ( −1, 3), (−4, 5), (−1,0)} ❖ FUNCTION A function is a set of ordered pairs (x, y) such that no two distinct members have the same first element. Is a special type of relation that for every input there corresponds a unique output. “All functions are relations, but not all relations are functions.” ❖ WAYS TO REPRESENT A FUNCTION I. NUMERICALLY = No two or more ordered pair have the same abscissa or x-coordinate 1. Set of ordered pairs 2. Table of values II. GRAPHICALLY 3. Graphs VERTICAL LINE TEST = A graph is a function if any vertical line drawn passing through the graph intersects the graph at exactly one point. 4. Mapping or Arrow Diagram 1  a. One – to – One Correspondence b. One – to – Many Correspondence c. Many – to – One Correspondence d. Many – to – Many Correspondence III. ALGEBRAICALLY = The exponent of the y variable should not be greater than one. 5. Given an Equation Example: 2𝑥 − 3𝑦 = 6 IV. VERBALLY 6. Rules of Correspondence = rules or formula expressed in words Example: The relation that exist between height & shoe size ❖ GENERALIZATION: When does a relation represent a function? Given an ordered pair or table of values: if and only if no two distinct members have the same first element.” Graph: Use the Vertical Line Test = the line intersects the graph at exactly one point Arrow Diagram/Mapping: Only One-to-One and Many-to-One are functions Equation: The exponent of the y variable should not be greater than 1. Rule of correspondence: Analyze the statement for the singularity or plurality of the word. ACTIVITY #2 Determine whether the following is a relation or a function. 1. 𝐴 = {(1, 3), (2, 5), (3, 9), (4, 11), (1, − 15)} 2. 𝐴 = {(0, − 4), (7, 1), (2, 5), (3, 1), (4, − 1)} 3. x –1 1 3 5 1 y 3 5 7 9 5 4. Automobiles and its plate number 13. 5. The students’ Learners Reference Number (LRN) 6. School’s rules & regulations to students 7. A person’s number of work hours to its salary 8. The speed with respect to the distance covered 14. 9. 𝑦 = √𝑥 2 − 1 10. 3𝑥 2 + 4𝑦 = 1 11. 5𝑥 2 + 2𝑦 3 = 0 12. 15. 𝑗 𝑝 𝑎 1 ⬚ ⬚ ⬚ ⬚ 𝑘 𝑞 𝑏 2 ⬚ ⬚ ⬚ ⬚ (𝑙) (𝑟) (𝑐) (3) nylecoj0914 Ms. Jocelyn P. dela Peña 2