Relations & Functions

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Vocabulary to begin a unit on functions and relations.

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Relations & Functions

  1. 1. Relations & Functions<br />
  2. 2. Ordered Pair<br />An ordered pair is a set of 2 numbers, <br />x and y, <br />also known as coordinates of a point on a graph<br />(x, y)<br />
  3. 3. Coordinate Plane<br />Quadrant I<br />Quadrant II<br />Quadrant III<br />Quadrant IV<br />
  4. 4. (+, +)<br />(-, +)<br />(+,-)<br />(-, -)<br />
  5. 5. Relation<br />Any set of ordered pairs<br />(-2, 8), (-1, 7), (-1, 6),(7, 6) <br />
  6. 6. Function<br />Any set of ordered pairs <br />in which <br />NO x value is repeated.<br />(-2, 8), (-1, 7), (0, -1),(7, 6)<br />* y values can be repeated<br />
  7. 7. Graphical Representations<br />Of a function or relation<br />
  8. 8. Set Notation – Ordered Pairs<br />{(-2,3),(0,-3),(2,-4),(7,0)}<br />*ordered pairs encompassed by braces<br />
  9. 9. Table of Values<br />
  10. 10. Mapping Diagram<br />x<br />f(x)<br />-2<br />-1<br />0<br />7<br />-1<br />3<br />6<br />7<br />
  11. 11. Graph<br />
  12. 12. The vertical line test<br />In order to use the vertical line test, you must first plot the points on a coordinate plane. <br />If you can draw a vertical line through each of the data points, and each line passes through EXACTLY one point, then the relation is a function.<br />
  13. 13. Using the vertical line test.<br />This is a function.<br />This is NOT a function.<br />y<br />y<br />x<br />x<br />
  14. 14. Domain<br />The set of x values in a <br />relation or function.<br />In the relation:<br />{(-2,3),(0,-3),(2,-4),(7,0)}<br />the domain is <br />{-2, 0, 2, 7}<br />
  15. 15. Range<br />The set of yvalues in a <br />relation or function.<br />In the relation:<br />{(-2,3),(0,-3),(2,-4),(7,0)}<br />the range is <br />{-4, -3, 0, 3}<br />
  16. 16. Function Notation<br />f(x)<br />Represents the function evaluated at x<br />Read “f of x”<br />
  17. 17. Function Rule <br />An equation that represents a function<br />f(x) = 6x – 2 <br />g(x) = -2x + 4<br />
  18. 18. Synonyms for “Domain”<br /><ul><li> Domain
  19. 19. Input
  20. 20. x
  21. 21. Independent variable</li></li></ul><li>Synonyms for “Range”<br /><ul><li> Range
  22. 22. Output
  23. 23. y
  24. 24. Dependent variable</li></li></ul><li>Wrap Up:<br />Write your answers on your worksheet <br />
  25. 25. What is a relation?<br />
  26. 26. What is a function?<br />
  27. 27. What are the 4 graphical representations of a function?<br />
  28. 28. What are the domain and range of a function or relation?<br />
  29. 29. How do you know a relation is a function?<br />
  30. 30. Describe the vertical line test?<br />
  31. 31. HOMEWORK<br />

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