introduction to function( general mathematics)

module 1 of general mathematics

1. Functions

2. Learning Target: Define a function Represents a function through set of ordered pairs, diagrams and graphs. Identify domain and range Representing real-life situations using functions, including piecewise function

3. What are some of the real- life applications of functions? Essential Question

4. Illustration DANIEL ENRIQUE RONNIE KATHRYN LIZA LOISA GERALD BEA JULIA MAJA KIM Which of the diagram shows a function? Function Not a function/ Relation

5. Relations and Functions Relations The elements of the domain can be imagined as input to a machine that applies a rule to these inputs to generate one or more outputs( range ). A relation is also a set of ordered pairs (x, y) Functions The elements of the domain can be imagined as input to a machine that applies a rule so that each input corresponds to only one output ( range ). Set of ordered pairs (x, y) such that no two ordered pairs have the same x –value but different y - values

6. FUNCTION as a Machine

7. FUNCTION Map FUNCTION RULE (Rule of Correspondence) The area A of a circle is a function of its radius r.   Domain Range All radii r All areas A   However, different elements in the set of inputs may produce the same elements in the set of outputs.

8. Functions are often denoted by any letter of the English alphabet or Greek character. The most commonly used notations are f, g, h, F, G, H, If is a function and is an element in its domain then it is denoted by  

9. Functions as a set of ordered pairs Which of the following sets of ordered pairs are functions? X = {(1, 1), (2, 2), (3, 3), (4, 4)} Z= {(-1, 2), (-2, 3), (1, 4), (2, 4)} Y= {(1, 3), (1, 4), (2, 5), (2, 6), (3, 7)} Function Not a Function Function A = {(1, 0), (0, 1), (-1, 0), (0, -1)} Not a Function

10. Functions as a mapping diagram 1 2 3 4 5 3 5 9 11 13 x y -2 -1 1 2 -1 4 5 -1 -2 -3 -4 x x y y Function Function Not a Function A B C

11. Functions as a graph Vertical line test * A graph represents a function if and only if each vertical line intersects the graph at most once

12. Not a Function Function Not a Function

13. Domain and Range of a Function Domain – set of inputs - set of all possible values that variable x can take - independent variable x Range – set of outputs - dependent variable y

14. Example #1 A = {(2, 5), (-4, 7), (6, 8)} Domain: {2, -4, 6} Range: {5, 7, 8}

15. Example #2 Domain: {1, 2, 3, 4, 5} Range: {3, 5, 9, 11, 13}

16. Example #2   Domain:   Range:   -1 1 -1 1 -1 1 -1 1 Table of Values

17. Example #3   -2 2 4 4 -2 2 4 4 Table of Values Domain:   Range:  

18. Example #4   -1 2 -1 undefined 0.5 -1 2 -1 undefined 0.5 Table of Values Domain:   Range:  

19. Functions as representation of real life Give a function that can represent the cost of buying meals, if one meals costs 40 pesos . Solution: Since each meal cost 40 pesos, then the cost function is  

20. 2. Maya has an internet service that currently has a monthly access fee of $11.95 and a connection fee of $0.50 per hour. Represent her monthly cost as a function of connection time. Let = the number of hours Maya spends on the internet in one month. = Maya’s monthly cost Function Rule:  

21. 3. What if your bank charges a monthly fee of $15 for your checking account and also charges $0.10 for each check written? How would you represent this scenario with a  function ? Function Rule:  

22. PIECEWISE- DEFINED FUNCTION

23. A videoke machine can be rented for 1000 pesos for three days, but for the fourth day onwards, and additional cost of 400 pesos per day is added. Represent the cost of renting a videoke machine as a piecewise function of the number of days it is rented. Let = number of days If if    

25. Thank you for listening