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Understanding Mathematical Relations and Functions

Learn about mathematical relations, functions, domain, range, one-to-one, onto, discrete vs. continuous, and more.

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Understanding Mathematical Relations and Functions

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  1. Bellwork: • Evaluate f(x)= 5x-3 for x=4 • Graph the following point on a graph. *Label Each* • (1, 3), (-1, 0), (1/2, -4), (0, 4)

  2. Solve for y: f(x)= 5x-3 for x=4 • f(4)= 5(4)-3 • f(4)=20-3 • f(4)=17 • b) Graph the following point on a graph. *Label Each* • (1, 3), (-1, 0), (1/2, -4), (0, 4) (0, 4) (1, 3) (-1, 0) (1/2, -4)

  3. 2-1: Relations and Functions Relations • What is a relationship? • In math a relation is a connection between a set of inputs and a set of outputs

  4. Representations (other than equations) • Ordered pairs: (-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5) 2) Table:

  5. 3) Graph (-3, -2) (5, 0) (0, 1) (-1, 4) (4, 5) (2, -5)

  6. 4) Mapping (-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5) -3 -1 0 2 4 5 -5 -2 0 1 4 5

  7. 4) Mapping (another way) (-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5) -3 -1 0 2 4 5 -5 -2 0 1 4 5

  8. Domain and Range • Domain- All inputs • Range- All outputs (-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5) Domain: -3, 5, 0, -1, 4, -5 Range: -5, -2, 0, 1, 4, 5

  9. Function • A function is a special kind of relation where every input goes to exactly one output • It’s PREDICTABLE! *Can be written using Function Notation:

  10. One-to-one • Every input has a unique output

  11. Onto • Every output has an input

  12. Discrete vs. Continuous • Discrete relation: A relation where the domain is a set of individual points • Continuous relation: A relation that can be graphed with a line or smooth curve

  13. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  14. {(2,3), (3,4), (5,1), (6,2), (2,4)} Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  15. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  16. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  17. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  18. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  19. {(2,3), (3,4), (5,1), (6,2), (3,3)} Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  20. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  21. Tom is Driving from Missouri to Georgia and his speed varies between 0 mph and 75mph at various distances from his starting point. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  22. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  23. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  24. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  25. The number of employees a company had in each year from 2004 to 2009 were 25, 28, 34, 31, 27, and 29. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  26. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  27. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

  28. Domain? Range? Function? One to one? Onto? Discrete or Continuous?

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