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are said to be if and only if and At the same time.

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Presentation on theme: "are said to be if and only if and At the same time."— Presentation transcript:

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3 are said to be if and only if and At the same time

4 TEST and

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14 are said to be if and only if and At the same time

15 are said to be if and only if THEY ARE INVERSE FUNCTIONS and

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27 FOLD

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30 y = x

31 (2, 0) FOLD OVER THE LINE

32 (2, 0) (0, 2)

33 (2, 0) (0, 2) (0,– 4) FOLD OVER THE LINE

34 (2, 0) (0, 2) (0,– 4) (– 4, 0)

35 (2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) FOLD OVER THE LINE

36 (2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6)

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38 (2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) The x’s and y’s traded places

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40 (2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) The x’s and y’s traded places

41 (2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) These points are called the INVERSES

42 Inverse Functions Are Reflections over the Line y = x

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44 Given the relation: FIRST IT MUST BE A

45 Given the relation:

46 It must be

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49 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 xy

50 xy Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 The Dependent and Independent Variables Trade Places INVERSE FUNCTION

51 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

52 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate 1 INVERSE FUNCTION xy

53 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 INVERSE FUNCTION xy

54 Independent Variable Abscissa Dependent Variable Ordinate -51 3 INVERSE FUNCTION Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 xy

55 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 INVERSE FUNCTION xy

56 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 4 INVERSE FUNCTION xy

57 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 -24 INVERSE FUNCTION xy

58 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 -24 INVERSE FUNCTION xy

59 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 -24 INVERSE FUNCTION xy

60 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2 Independent Variable Abscissa Dependent Variable Ordinate -51 -33 -24 INVERSE FUNCTION xy

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62 Is it a FUNCTION? Is it a ONE-TO-ONE?

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64 INVERSE FUNCTION

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68 Find The Equation of the Line

69 y = 2 x – 4

70 Find The Equation of the Line y = 2x – 4

71 y = ½ x + 2

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73 INVERSE FUNCTION

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75 Any Vertical Line Drawn Intersects The Graph No More Than Once

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77 Any Horizontal Line Drawn Intersects The Graph No More Than Once

78 INVERSE FUNCTION

79 Independent Variable Abscissa Dependent Variable Ordinate 1-5 3-3 4-2

80 The Dependent and Independent Variables trade places

81 Solve For The New y

82 INVERSE FUNCTION

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84 FUNCTION

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86 Match y = 2x – 4 y = ½ x + 2

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92 The Dependent and Independent Variables trade places

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101 The Dependent and Independent Variables trade places

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111 The Dependent and Independent Variables trade places

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120 () () When you put in into the Calculator

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122 The Dependent and Independent Variables trade places

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