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Math 71A

Explore functions and relations through ordered pairs, domains, ranges, and functions as equations. Learn to identify functions based on inputs and outputs.

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Math 71A

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  1. Math 71A 2.1 and 2.2 – Functions

  2. Relations The number of Drug Law Violations per year at Mt. SAC is given by the following table: (Source: http://www.mtsac.edu/safety/stats/)

  3. Relations The number of Drug Law Violations per year at Mt. SAC is given by the following table: (Source: http://www.mtsac.edu/safety/stats/) We can write this as a set of ordered pairs (called a ______________): {(2007, 3), (2008, 4), (2009, 2), (2010, 4)}

  4. Relations The number of Drug Law Violations per year at Mt. SAC is given by the following table: (Source: http://www.mtsac.edu/safety/stats/) relation We can write this as a set of ordered pairs (called a ______________): {(2007, 3), (2008, 4), (2009, 2), (2010, 4)}

  5. Relations {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} The set of all the first components is called the ______________. Above, it is _________________. The set of all the second components is called the ___________. Above, it is _______________.

  6. Relations {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} The set of all the first components is called the ______________. Above, it is _________________. The set of all the second components is called the ___________. Above, it is _______________. domain

  7. Relations {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} The set of all the first components is called the ______________. Above, it is _________________. The set of all the second components is called the ___________. Above, it is _______________. domain {2007, 2008, 2009, 2010}

  8. Relations {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} The set of all the first components is called the ______________. Above, it is _________________. The set of all the second components is called the ___________. Above, it is _______________. domain {2007, 2008, 2009, 2010} range

  9. Relations {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} The set of all the first components is called the ______________. Above, it is _________________. The set of all the second components is called the ___________. Above, it is _______________. domain {2007, 2008, 2009, 2010} range {3, 4, 2}

  10. Relations Relations can be visualized like this (called an “arrow diagram”):

  11. Relations Ex 1.Find the domain and range of the relation {(3, 5), (-2, 1), (3,7), (0, 5)}.

  12. Relations Ex 1.Find the domain and range of the relation {(3, 5), (-2, 1), (3,7), (0, 5)}. Domain: {3, -2, 0}

  13. Relations Ex 1.Find the domain and range of the relation {(3, 5), (-2, 1), (3,7), (0, 5)}. Domain: {3, -2, 0} Range: {5, 1, 7}

  14. Functions A relation in which each member of the domain corresponds to exactly one member of the range is called a ____________________.

  15. Functions A relation in which each member of the domain corresponds to exactly one member of the range is called a ____________________. function

  16. Functions A relation in which each member of the domain corresponds to exactly one member of the range is called a ____________________. function (That is, each input has only one output.)

  17. Functions ex: {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} is a function since each input has only one output. ex: {(3, 5), (-2, 1), (3,7), (0, 5)} is not a function since 3 has two outputs: ___ and ___.

  18. Functions ex: {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} is a function since each input has only one output. ex: {(3, 5), (-2, 1), (3,7), (0, 5)} is not a function since 3 has two outputs: ___ and ___.

  19. Functions ex: {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} is a function since each input has only one output. ex: {(3, 5), (-2, 1), (3,7), (0, 5)} is not a function since 3 has two outputs: ___ and ___. 5 7

  20. Functions ex: {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} is a function since each input has only one output. ex: {(3, 5), (-2, 1), (3,7), (0, 5)} is not a function since 3 has two outputs: ___ and ___. 5 7

  21. Functions ex: {(2007, 3), (2008, 4), (2009, 2), (2010, 4)} is a function since each input has only one output. ex: {(3, 5), (-2, 1), (3,7), (0, 5)} is not a function since 3 has two outputs: ___ and ___. 5 7

  22. Functions as Equations For this class, we’ll focus on functions in the form of equations. For example,

  23. Functions as Equations We often give functions names (like ) and use special notation to define them.

  24. Functions as Equations For example, . is read “ of ”. represents the value of the function at (that is, the output of ). For example, , that is “ of is ”. So, if you input 2, the output is 0.

  25. Functions as Equations For example, . is read “ of ”. represents the value of the function at (that is, the output of ). For example, , that is “ of is ”. So, if you input 2, the output is 0.

  26. Functions as Equations For example, . is read “ of ”. represents the value of the function at (that is, the output of ). For example, , that is “ of is ”. So, if you input 2, the output is 0.

  27. Functions as Equations For example, . is read “ of ”. represents the value of the function at (that is, the output of ). For example, , that is “ of is ”. So, if you input 2, the output is 0.

  28. Functions as Equations Ex 2.Find for the function h. Ex 3.Find for . Ex 4.Find for .

  29. Functions as Tables What are the domain and range? Find such that .

  30. Functions as Tables What are the domain and range? Find such that .

  31. Functions as Tables What are the domain and range? Find such that . Domain: {-2, -1, 0, 1, 2} Range: {4, 1, 0}

  32. Functions as Tables What are the domain and range? Find such that . Domain: {-2, -1, 0, 1, 2} Range: {4, 1, 0}

  33. Functions as Tables What are the domain and range? Find such that . Domain: {-2, -1, 0, 1, 2} Range: {4, 1, 0}

  34. Functions as Tables What are the domain and range? Find such that . Domain: {-2, -1, 0, 1, 2} Range: {4, 1, 0}

  35. Functions as Tables What are the domain and range? Find such that . Domain: {-2, -1, 0, 1, 2} Range: {4, 1, 0} or

  36. Interval Notation Suppose you wanted to write “the set of all real numbers between 3 and 5, including 3, but not 5.” That is, the set of all real numbers , such that . Here’s how to write it using interval notation: ___________________

  37. Interval Notation Suppose you wanted to write “the set of all real numbers between 3 and 5, including 3, but not 5.” That is, the set of all real numbers , such that . Here’s how to write it using interval notation: ___________________

  38. Interval Notation Suppose you wanted to write “the set of all real numbers between 3 and 5, including 3, but not 5.” That is, the set of all real numbers , such that . Here’s how to write it using interval notation: ___________________

  39. Interval Notation Suppose you wanted to write “the set of all real numbers between 3 and 5, including 3, but not 5.” That is, the set of all real numbers , such that . Here’s how to write it using interval notation: ___________________

  40. Ex 6.

  41. Ex 6.

  42. Ex 6.

  43. Ex 6.

  44. Ex 6.

  45. Ex 6.

  46. Ex 6.

  47. Ex 6.

  48. Ex 6.

  49. Ex 6.

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