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Functions 3.5

Functions 3.5. An Introduction to Funtions. Independent and Dependent Variables. Independent and Dependent Variables. Definitions Indepdent Variable: the variable that someone/something changes directly Dependent Variable: the result of the independent variable changing.

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Functions 3.5

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  1. Functions 3.5 An Introduction to Funtions

  2. Independent and Dependent Variables

  3. Independent and Dependent Variables Definitions Indepdent Variable: the variable that someone/something changes directly Dependent Variable: the result of the independent variable changing

  4. Independent and Dependent Variables independent(cause) dependent(effect) Examples: ind: hours I study for class dep: grade in class

  5. Independent and Dependent Variables ind: hours I worked in a pay period dep: how much I got paid

  6. Independent and Dependent Variables ind: amount of time spent on the treadmill this week dep: blood pressure

  7. Independent and Dependent Variables There is a relationship between the independent and dependent variable This relationship can be shown using an ordered pair (x,y) (cause, effect)

  8. Functions

  9. Functions Function: a relation in which, for each value of the first component there is exactly one value of the second component Example: Remote control (x,y) (cause, effect)

  10. Functions You can create your own function F={(1,1), (2,2),(3,3),(4,4)} This is a function because . . . ?

  11. Functions Function or Not a Function Is H a function? Why or Why not? H={(4,12),(3,7),(5,23)}

  12. Functions Function or Not a Function Is H a function? Why or Why not? H={(4,12),(3,7),(5,23)}

  13. Functions Function or Not a Function Is G a funtion? G={(1,1),(2,5),(3,7),(4,1)}

  14. Functions Function or Not a Function Is G a funtion? G={(1,1),(2,5),(3,7),(4,1)} Look closely at G You can have the same out put for different inputs Just as on your computer you can have two buttons(input) do the same action(output) Example: (Shift Key)

  15. Real World Functions Assume You own a resturant You require the host to always say "Welcome. How many will be in your party today?", every time someone walks through the door. This is a function (input, output) H = ([Person enters door], [Greeting]) Greeting customersdepends on people walking through the front door. Only greet customers when someone enters!!!

  16. Real World Functions Usher at the movie When ever a movie end, clean the theater U = (Movie Ends, Clean Theater) cleaning of the theaterdepends on the moving ending. Only clean the theater when the movie ends!

  17. Real World Functions Any other examples of functions?

  18. Functions Function only if for every input there is one output D = {(2,5), (3,4), (1,8) (2,7), (4,5)} Why is this not a function? Think back to remote control.

  19. Functions Function only if for every input there is one output D = {(2,5), (3,4), (1,8) (2,7), (4,5)} Why is this not a function? Think back to remote control.

  20. Functions Function of Not a Function? {(1,2),(3,4),(5,6)} Function or Not a Function Why?

  21. Functions Function of Not a Function? {(1,2),(3,4),(5,6)} Function or Not a Function Why?

  22. Functions Function of Not a Function {(1,2), (2,2), (3,2), (4,2), (5,2) } Why?

  23. Functions Function of Not a Function {(1,2), (2,2), (3,2), (4,2), (5,2) } Why? Function

  24. Functions Function of Not a Function {(1,2), (2,2), (3,2), (4,7), (3,8) } Why?

  25. Functions Function of Not a Function {(1,2), (2,2), (3,2), (4,7), (3,8) } Why? Not a Function

  26. Functions Function of Not a Function {(2,4), (6,8), (10,12), (14,16), (18,20) } Why?

  27. Functions Function of Not a Function {(2,4), (6,8), (10,12), (14,16), (6,20) } Why? Not a Function

  28. Functions Function of Not a Function {(1,4), (2,8), (12,12), (7,4), (8,8) } Why?

  29. Functions Function of Not a Function {(1,4), (2,8), (12,12), (7,4), (8,8) } Why? Function

  30. Domain and Range

  31. Domain and Range The domain is set of all values of the independent variable(x) The range is the set of all values of the dependent variable(y)

  32. Domain and Range Example {(1,2),(3,4),(5,6),(7,8)} Domain is{1,3,5,7} First Component of the ordered pair Range is {2,4,6,8} Second Component of the ordered pair

  33. Domain and Range What is the Domain and Range? {(1,7), (10,16), (4,-2)} Domain? Range?

  34. Domain and Range What is the Domain and Range? {(1,7), (10,16), (4,-2)} Domain {1, 4, 10} Range {-2, 7, 16, }

  35. Domain and Range What is the Domain and Range? {(-5, 31), (6,-1), (-7,-18)} Domain? Range?

  36. Domain and Range What is the Domain and Range? {(-5, 31), (6,-1), (-7,-18)} Domain {-7, -5, 6} Range {-18 ,-1 31}

  37. Domain and Range What is the Domain and Range? {(0 -3), (4,-3), (-4,0)} Domain? Range?

  38. Domain and Range What is the Domain and Range? {(0 -3), (4,-3), (-4,0)} Domain {-4, 0, 4} Range {-3,0}

  39. Domain and Range What is the Domain and Range? {(1, 2), (2,2), (3,2)} Domain? Range?

  40. Domain and Range What is the Domain and Range? {(1, 2), (2,2), (3,2)} Domain {1, 2, 3} Range {3}

  41. Finding Domains and Ranges From a Graph

  42. Finding Domains and Ranges From a Graph What is the domain and range? Domain {-1, 1, 2 } Range {-1, 1, 2}

  43. Finding Domains and Ranges From a Graph Try on your own. What is the domain and range Domain Range

  44. Finding Domains and Ranges From a Graph • Try on your own. • What is the domain and range • Domain {-4, -2, 3} • Range {-2, -1, 1}

  45. Finding Domains and Ranges From a Graph What is the domain and Range of this graph? Domain? Range?

  46. Finding Domains and Ranges From a Graph • Try on your own • What is the domain and Range of this graph? • Domain [-2, 2] • Range [-1, 4]

  47. Finding Domains and Ranges From a Graph Try on your own What is the domain and Range of this graph? Domain? Range?

  48. Finding Domains and Ranges From a Graph What is the domain and range for this graph Arrow heads mean continue indefinitely Domain(-∞, ∞) Range (-∞, ∞)

  49. Finding Domains and Ranges From a Graph Try This One What is the domain and range for this graph? Arrow heads mean continue indefinitely Domain(-∞, ∞) Range (-∞, ∞)

  50. Finding Domains and Ranges From a Graph What is the domain and range for this graph? Arrow heads mean continue indefinitely Domain(-∞, ∞) Range [-1, ∞)

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