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Absolute and Reciprocal Functions Unit 9

Absolute and Reciprocal Functions Unit 9
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2016-09-07 11:07
FunctionCoordinate GeometryCalculusDerivativeGraphing
This example demonstrates the graphs of absolute value and reciprocal functions, including their intersections. Key math concepts involve functions, absolute value, reciprocals, coordinate geometry, and differential calculus. GeoGebra commands used include Point, Intersect, Vector, and OrthogonalLine, with objects like f, g, c, b_1, h_3, etc. It is suitable for high school mathematics instruction and function graph analysis.

GeoGebra Commands & Parameters

  1. Point(b_3) → A
  2. Point(b_3) → C
  3. Point(b_3) → D
  4. Intersect(g_1, f_1, (4.000000000000211, 0.9999999999998943)) → E
  5. Intersect(g_1, f_1, (4.7823136094842975E-17, -1)) → F
  6. Point(p_1) → G
  7. Point(p_1) → H
  8. Point(p_1) → I
  9. Point(p_1) → J
  10. Point(r_1) → N
  11. Point(r_1) → O
  12. Point(r_1) → K
  13. Point(r_1) → L
  14. Point(s_1) → M
  15. Point(s_1) → P
  16. Point(s_1) → Q
  17. Point(s_1) → R
  18. Intersect(c, yAxis, 1) → S
  19. Intersect(c, xAxis, 2) → T
  20. Intersect(c, xAxis, 1) → U
  21. Point(b_1) → V
  22. Point(xAxis) → infinity_-
  23. Point(xAxis) → infinity_+
  24. Intersect(xAxis, yAxis) → origin
  25. Vector(origin, infinity_-) → domain_-
  26. Vector(origin, infinity_+) → domain_+
  27. Vector(origin, infinity_P) → range_P
  28. Point(yAxis) → infinity_N
  29. Vector(origin, infinity_N) → range_N
  30. Point(a_2) → F_1
  31. Point(g_2) → H_1
  32. Intersect(f, xAxis) → I_1
  33. Intersect(f, yAxis) → J_1
  34. Intersect(g, yAxis, (0, 6)) → K_1
  35. Intersect(g, xAxis, (-2, 0)) → L_1
  36. Intersect(h_3, xAxis, (-2, 0)) → M_1
  37. Intersect(h_3, xAxis, (2, 0)) → N_1
  38. Intersect(p, yAxis, (0, 1)) → W
  39. Intersect(u, ((-(x(xAxis) / y(xAxis))) * x) - z(xAxis) / y(xAxis), 2) → B_1
  40. Intersect(i, xAxis) → C_1
  41. Intersect(b_3, ((-(x(xAxis) / y(xAxis))) * x) - z(xAxis) / y(xAxis), 1) → D_1
  42. Intersect(e, ((-(x(xAxis) / y(xAxis))) * x) - z(xAxis) / y(xAxis), 1) → E_1
  43. OrthogonalLine(origin, xAxis) → f_2
  44. Intersect(j, ((-(x(xAxis) / y(xAxis))) * x) - z(xAxis) / y(xAxis), 1) → G_1
  45. Intersect(j, ((-(x(xAxis) / y(xAxis))) * x) - z(xAxis) / y(xAxis), 2) → O_1
  46. Intersect(q, k_3, (2.666666666969492, 0.9999999990915249)) → P_1
  47. Intersect(q, k_3, (2.000000000002484, -1.0000000000074518)) → Q_1
  48. Intersect(l, i_2) → R_1
  49. Intersect(s, r, 1) → S_1
  50. Intersect(s, r, 2) → T_1
  51. Intersect(s, r, 2) → U_1
  52. Intersect(s, r, 2) → V_1
  53. Intersect(s, r, 2) → W_1
  54. Intersect(s, r, 2) → Z_1
  55. Point(s) → A_2
  56. Intersect(g_1, f_1, (4, 1)) → B_2
  57. Intersect(g_1, f_1, (0, -1)) → C_2
  58. Intersect(p_1, c_1, 1) → D_2
  59. Intersect(p_1, c_1, 4) → E_2
  60. Intersect(p_1, c_1, 2) → F_2
  61. Intersect(p_1, c_1, 3) → G_2
  62. Intersect(c_1, yAxis, 1) → H_2
  63. Intersect(p_1, yAxis, (0, -0.25)) → I_2
  64. Intersect(q_1, k_1, (-2, 1)) → J_2
  65. Intersect(q_1, k_1, (-4, -1)) → K_2
  66. Intersect(s_2, t_2) → L_2
  67. Intersect(r_1, d_1, 2) → M_2
  68. Intersect(r_1, d_1, 3) → N_2
  69. Intersect(r_1, d_1, 4) → O_2
  70. Intersect(r_1, d_1, 1) → P_2
  71. Intersect(r_1, l_1, (-3, 0.5)) → Q_2
  72. Intersect(d_1, l_1, 1) → R_2
  73. Intersect(d_1, n_1, 1) → S_2
  74. Intersect(d_1, m_1, 1) → T_2
  75. Intersect(s_1, e_1, 2) → U_2
  76. Intersect(s_1, e_1, 1) → V_2
  77. Intersect(s_1, e_1, 3) → W_2
  78. Intersect(s_1, e_1, 4) → Z_2
  79. Intersect(f_3, i_3, (0, 0)) → E_3
  80. Intersect(f_3, j_3, (0, 0)) → F_3
  81. Intersect(q_3, c_3, 3) → D_3
  82. Intersect(q_3, c_3, 1) → H_3
  83. Intersect(c_3, r_3, 1) → I_3
  84. Intersect(q_3, r_3, (-1.1, 0.5882352941176471)) → J_3
  85. Intersect(c_3, s_3, 1) → K_3
  86. Intersect(c_3, s_3, 2) → L_3
  87. Intersect(c_3, t_3, 2) → M_3
  88. Intersect(c_3, s_3, 2) → N_3
  89. Point(p) → Q_3
  90. Point(p) → R_3
  91. Intersect(c_3, d_3, 2) → Z
  92. Intersect(c_3, d_3, 1) → A_1
  93. OrthogonalLine(Z, a_3) → f_4
  94. OrthogonalLine(A_1, a_3) → g_4