Pre algebra lesson 8-1

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Pre algebra lesson 8-1

  1. 1. Relations and FunctionsObjective: To use tables and graphsto represent relations and functions.
  2. 2. 5-Minute CheckSolve each equation or inequality.2. 3x – 2 = 13
  3. 3. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5
  4. 4. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21
  5. 5. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3
  6. 6. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3
  7. 7. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3 x = -2
  8. 8. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3 x = -2• -12x > -24
  9. 9. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3 x = -2• -12x > -24 x<2
  10. 10. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3 x = -2• -12x > -24 x<2• 7x < 2x – 25
  11. 11. 5-Minute CheckSolve each equation or inequality.• 3x – 2 = 13 x=5• 6 – 5x = 21 x = -3• (2x + 7)/3 = x + 3 x = -2• -12x > -24 x<2• 7x < 2x – 25 x < -5
  12. 12. Relations and FunctionsA Relation is a set of ordered pairs. The set of thefirst coordinates is called the domain of therelation. The set of the second coordinates iscalled the range of the relation.
  13. 13. Relations and Functions x yExample: -4 5 -2 6 0 2
  14. 14. Relations and Functions x yExample: -4 5 -2 6Domain: {-4, -2, 0} 0 2
  15. 15. Relations and Functions x yExample: -4 5 -2 6Domain: {-4, -2, 0} 0 2Range: {5, 6, 2}
  16. 16. Relations and FunctionsA Function is a relation in which each element ofthe domain is paired with exactly one element inthe range.
  17. 17. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  18. 18. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  19. 19. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  20. 20. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  21. 21. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  22. 22. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  23. 23. Relations and Functions x y -4 5Example: -2 6 0 2 1 7 3 -5
  24. 24. Relations and Functions x y -4 5 Example: -2 6 0 2 1 7 3 -5The vertical line test can be used to determine if therelation is a function. Use a straight edge moved slowlyacross the graph to see if two point touch the edge atthe same time. This is a true test for all functions.
  25. 25. Relations and Functions5. x y 3 -4 Example: -1 7 -6 -8 1 11 4 13
  26. 26. Relations and Functions x y 3 -4Example: -1 7 -6 -8 1 11 4 13 Domain: {-6,-1,1,3,4} Is this relation a function? Range: {-8,-4,7,11,13}
  27. 27. 6. x y 0 -2 Example: -2 1 3 -2 -4 4 1 -3
  28. 28. 6. x y 0 -2 Example: -2 1 3 -2 -4 4 1 -3 Domain: {-4,-2,0,1,3} Is this relation a Range: {-3,-2,1,4} function?
  29. 29. 7. x y 0 4 Example: -1 4 -1 3 -1 0 5 1
  30. 30. 7. x y 0 4 Example: -1 4 -1 3 -1 0 5 1 Domain {-1,0,5} Is this relation a Range {0,1,3,4} function?

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