Introduction to Functions PDF

 DAY 1 Introduction to General Mathematics  LEARNING COMPETENCIES Solve operation Identify the of integers. different ways Recall the...

 DAY 1 Introduction to General Mathematics  LEARNING COMPETENCIES Solve operation Identify the of integers. different ways Recall the of expressing a concept of Determine if the functions and classification of given relation relation. Number System. represents a function.  REAL NUMBERS  COMPLEX NUMBERS NUMBER SYSTEM REAL NUMBERS IMAGINARY NUMBERS (4,7,0,2, 11) (i) RATIONAL NUMBERS “any number that can be expressed as a quotient/ratio” (-3, 4/5, 6/7, -8/5, 0, 11/2) INTEGERS NON-INTEGERS “not fraction or decimal” “fraction & decimal” (1, 3, 5, -5, -6, -7, 0) (1/2, ¾, -5/8) WHOLE NUMBERS NEGATIVE NUMBERS “consist of the natural numbers & 0” (0, 1, 2, 3, 4, …) ( -1, -2, -3) COUNTING ZERO NUMBERS (0) (1, 2, 3, 4, 5, …) INSTRUCTION: Identify whether the statement about the number system is TRUE or FALSE. TRUE 1. All counting numbers are whole numbers. TRUE 2. All integers are rational numbers. TRUE 3. A number can be rational and irrational. FALSE 4. Every decimal number is an irrational number. FALSE 5.All real numbers are rational numbers. INTEGERS  INTEGERS Definition: Integers are whole numbers that describe opposite ideas in mathematics. Negative 0 Positive  OPERATION OF INTEGERS Rules for the operation of integers: Addition: Subtraction: Same sign add and Different sign subtract and copy keep there sign. the sign of the bigger number.  OPERATION OF INTEGERS Rules for the operation of integers: Multiplication: Division: Same sign = positive result Different sign = negative result INSTRUCTION: Choose the letter of your answer and input it on the chat box. A. 31 B. 41 INSTRUCTION: Choose the letter of your answer and input it on the chat box. A. 6 C. -24 B. -6 D. 24 INSTRUCTION: Choose the letter of your answer and input it on the chat box. A. -21 B. -39 INSTRUCTION: Choose the letter of your answer and input it on the chat box. A. 24 B. -24 INSTRUCTION: Choose the letter of your answer and input it on the chat box. A. 7 B. -7  DAY 1 Illustrating Functions and Relations  RELATION Domain (x): { 1, 2, 3, 4, 5} Input Range (y): {1, 3, 5, 7, 9} Output  RELATION Table of Mapping Values x y x y 1 1 1 1 2 3 2 3 3 5 3 5 4 7 4 7 5 9 5 9  KINDS OF RELATION x y x y x y 1 1 1 1 1 1 2 3 3 2 3 5 5 3 5 4 7 3 7 4 5 9 9 5 9 One to one One to many Many to one  FUNCTIONS Definition: - Is a rule that pairs each element in one set, called the domain, with exactly one element from a second set called range. FUNCTION NOT A FUNCTION  KINDS OF RELATION One to one One to many Many to one x y x y x y 1 1 1 1 1 1 2 3 3 2 3 5 5 3 5 4 7 3 7 4 5 9 9 5 9 One-to-one and many-to-one relations can be considered as functions.  POINTS TO PONDER ❑All functions are relation, but not all relations are function. ❑One-to-one and many-to-one relations can be considered as functions. DIFFERENT WAYS IN EXPRESSING FUNCTION AND RELATION Set of Ordered Pairs Table of values Mapping Graphs Equation  GRAPH ❑The vertical line test is a method that is used to determine whether a given relation is a function or not  EQUATION We can consider an equation a function if: 1. There is y in the equation. 2. The exponent of y is an odd number. 3. Y is not in the absolute value symbol; and 4. The relationship is in equality form. Determine if the following relations represent a function or not a function. 11.{(q, 0), (w, 1), (e, 2), (t, 3)} function 12.{(-1, -2), (0, -2), (1, -2), (2, -2)} function 13.{(1, 0), (1,1), (1, 2), (1, -2)} not a function 14.{(x, 3), (y, 4), (z, 3), (w, 4)} function Determine if the following relations represent a function. 15. 16. function not a function Determine if the following relations represent a function. function Determine if the following relations represent a function. not a function Determine if the following relations represent a function. not a function Determine if the following relations represent a function. function  REMINDER 1. Materials will be posted in the google classroom. 2. Check your google classroom during your asynchronous time.