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Relations and Functions

Relations and Functions. Georgia Performance Standard (GPS): MM4A1 “Students Will Explore Rational Functions.”. GPS MM4A1.

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Relations and Functions

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  1. Relations and Functions Georgia Performance Standard (GPS): MM4A1 “Students Will Explore Rational Functions.”

  2. GPS MM4A1 • Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior. • Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

  3. GPS MM4A1 C. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

  4. EQ: • What is a function and how do I recognize it?

  5. Vocabulary • Relation: a set of ordered pairs – each x-value is paired with one or more y-values • Function: a set of ordered pairs, no x-value is repeated – each x-value is paired with exactly one y-value • Vertical Line Test: the graph of a relation represents a function if no vertical line intersects more than one point on the graph at the same time

  6. Continued… • Domain – all x-values • Range – all y-values

  7. Example 1 • Does { (1,3) (2,5) (3,4) (2,-6) } represent a function? • YES or NO? • What is the domain? • What is the range?

  8. Example 2 • Is the following a function?

  9. Example 3, 4, and 5 • Function?

  10. Evaluate • “Evaluate” means to solve EX. 6: Evaluate each function for the given values of x f(x)=2x-3 for x=1 and x=-3

  11. Assignment: • Pg. 107, #’s 5-10 and pg. 108, #’s 16-50 all

  12. Answers 5. No 6. Yes 7. Yes 8. No 9. Yes 10. No 16. Yes 17. Yes 18. No 19. Yes 20. Yes 21. Yes 22. Yes 23. Yes 24. No 25. No 26. No 27. Yes 28. No 29. Yes 30. No 31. Yes 32. Nope

  13. Answers continued… 33. No 34. Yes 35. Yes 36. No 37. D: 0, 3 R: 2, 4 38. D: 1, 2, 3 R: 5 39. D: 7, 8, 9 R: -3, -2, -1 40. D: 4, 5, 6 R: 1, 2, 3 41. D: 4, 5, 6 R: -6, -5, -4 42. D: 0, 1.5, 2.5 R: 0 43. -4; 0 44. 2; -4 45. -1; 1/3 46. -13/5; 1 47. 9; 20 48. 3; 2.75 49. 1/3; 3/16 50. -9; -16

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