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Function powerpoinr.pptx
- 1. Four Pics one word
- 2. Four Pics one word
- 4. 1. Domain is the set of all x or input values. Reveal Answer YES NO 2. Set is a collection of well-defined and distinct objects, called elements that share a common characteristics. 3. Range is the set of all x input values. 4. Ordered pair is a pair of objects taken in a specific order.
- 5. 5 Relation is a rule that relates values from a set of values (domain) to a second set of values (range). Reveal Answer YES NO 6. In the given relation, the domain value 0 corresponds to the range value -2? {(-1,2), (-2,4), (2,5), (0,-2), (2,0)}. 7. {(0,2), (1,3), (4,3), (1,2)}, is an example of a function.
- 6. What do you need to know? 1 determine functions and relations; 2 illustrate functions through mapping diagram, sets and graphs; and 3 represent real-life situations using functions.
- 7. Ordered pair An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. (1,2)
- 8. Sets A set is a collection of objects, called the elements or members of the set. 1 2 3 6 4 5 1,2,3,4,5,6 , , , , , b d e g a f
- 9. What is relation? A relation is a set of ordered pairs. If you limit it to points in the Cartesian Plane, it is a set of ordered pairs (, ) such that and belongs to the set of real numbers .
- 10. Example { , , , , , , , , , , , , , } Domain (x) is the set of all first coordinates. Range (y) is the set of all second coordinates. Domain Range {-1,0,1,2,4} {-5,-4, -3, -1,3, 5}
- 11. Representation of relation Example: { , , (2,3), (3,4) ,(, ) Table of Values X Y 1 1 2 3 3 4 4 5 1 2 3 4 1 3 4 5 X Y Mapping Graphing
- 12. Types of relation 1 2 3 4 1 3 4 5 X Y One to One Relation 1 5 1 3 4 5 X Y One to Many Relation 1 2 3 4 1 X Y Many-to -one Relation
- 13. What is function? = X = 1 ()= 2 () = 3 () = 4 () = = = = 倹 ≠ ＄ 腫
- 14. What is function? Independent set Dependent set
- 15. What is function? A function is a set of ordered pairs in which no two ordered pairs have the same first component but different second components.
- 16. Example 3 6 9 12 15 4 8 12 16 X Y Not a function 1 2 3 4 1 X Y Function 1 2 3 4 1 3 4 5 X Y Function
- 17. Example Functions as a set of ordered pairs Functions as equations Functions as graphs Functions as table of values = { 1,1 , 3,5 , 4,6 , 8,9 = { 1,0 , 2,0 , 1,5 = 2 + 1 = 4 5
- 18. Vertical l I ne test The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
- 19. Examples
- 20. Examples
- 21. Examples
- 22. Relatio n Function Note: All functions are relations, but not all relations are functions.
- 23. Function limitation Input Output x = 賊 4 賊2 9 賊3 16 賊4 25 賊5 =x Not a function = 賊
- 24. Application in real life Water bill depends on water consumption. Speed is a function of time and distance travelled. Revenue is based on the price and the number of products sold. A vending machined A soda, snack, or stamp machine the user puts in money, punches specific button, and a specific item drops into the output slot.
- 25. Application 1. Let = { 1,2 , 3,4 , 5,11 , 3,1 . Find the domain and range of the given relation. 2. In everyday life, you encounter many relations which may or may not represent a functions. Which of the following everyday relations are functions. a. is a daughter of ( and y are women). b. is taller that ( and are residents of the Philippines) c. has received a dental treatment from ( and are professionals) d. is a digit (0,9) on a telephone dial pad and is a corresponding letter. 3. Find the function value given the particular values of . a. = 2 11; 1 b. = 22 7; (2)
- 26. Assignment Please study the operations in function. In a short bond paper write the five operations on functions and give one example with complete solution.