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Function Addition Demonstration

Function Addition Demonstration
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2020-02-02 10:57
VectorFunctionCoordinate Geometry
This example demonstrates how to construct a graphical representation of function addition using GeoGebra. It involves core math concepts like functions, vectors, and coordinate geometry. Key GeoGebra commands used include Point, Intersect, and Vector. Suitable for high school mathematics education to understand the geometric meaning of function operations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → G
  3. Point(xAxis) → H
  4. Point(xAxis) → I
  5. Point(xAxis) → J
  6. Point(xAxis) → K
  7. Intersect(xAxis, yAxis) → L
  8. Point(yAxis) → M
  9. Point(yAxis) → S
  10. Point(xAxis) → O_1
  11. Point(xAxis) → P_1
  12. Point(xAxis) → Q_1
  13. Vector(A, K) → u
  14. Vector(B, J) → v
  15. Vector(C, I) → w
  16. Vector(D, H) → a
  17. Vector(E, G) → b
  18. Vector(F, M_1) → c
  19. Vector(M, J) → d
  20. Vector(N, I) → e
  21. Vector(O, H) → f
  22. Vector(P, G) → g
  23. Vector(Q, M_1) → h
  24. Vector(R, N_1) → i
  25. Vector(S, I) → j
  26. Vector(T, H) → k
  27. Vector(U, G) → l
  28. Vector(V, M_1) → m
  29. Vector(W, N_1) → n
  30. Vector(Z, O_1) → p
  31. Vector(A_1, P_1) → q
  32. Vector(L_1, Q_1) → r
  33. Vector(K_1, P_1) → s
  34. Vector(J_1, O_1) → t
  35. Vector(I_1, N_1) → u_1
  36. Vector(H_1, M_1) → v_1
  37. Vector(E_1, G) → w_1
  38. Vector(F_1, H) → a_1
  39. Vector(G_1, G) → b_1
  40. Point(yAxis) → R_1
  41. Point(yAxis) → F_2
  42. Point(yAxis) → R_2
  43. Point(xAxis) → Z_2
  44. Point(xAxis) → A_3
  45. Point(xAxis) → C_3
  46. Point(xAxis) → D_3
  47. Point(xAxis) → E_3
  48. Point(xAxis) → F_3
  49. Point(xAxis) → G_3
  50. Vector(S_1, L) → c_1
  51. Vector(W_2, L) → d_1
  52. Vector(T_1, K) → e_1
  53. Vector(B_2, K) → f_1
  54. Vector(Q_2, K) → g_1
  55. Vector(K_2, J) → h_1
  56. Vector(Z_1, I) → i_1
  57. Vector(W_1, H) → j_1
  58. Vector(V_2, Z_2) → k_1
  59. Vector(U_2, A_3) → l_1
  60. Vector(T_2, B_3) → m_1
  61. Vector(S_2, C_3) → n_1
  62. Vector(R_2, D_3) → p_1
  63. Vector(D_4, E_3) → q_1
  64. Point(xAxis) → I_4
  65. Point(xAxis) → J_4
  66. Vector(E_4, F_3) → r_1
  67. Vector(F_4, G_3) → s_1
  68. Vector(G_4, I_4) → t_1
  69. Vector(H_4, J_4) → u_2
  70. Vector(K_4, L) → v_2
  71. Vector(K_5, L) → w_2
  72. Vector(L_4, Z_2) → a_2
  73. Vector(B_5, Z_2) → b_2
  74. Vector(A_5, A_3) → c_2
  75. Vector(P_4, B_3) → d_2
  76. Vector(O_4, C_3) → e_2
  77. Vector(J_5, K) → f_2
  78. Vector(I_5, J) → g_2
  79. Vector(H_5, I) → h_2
  80. Vector(G_5, H) → i_2

AI Drawing Prompt Reference

On a coordinate plane, place several points on the y-axis and x-axis, and mark the origin at their intersection. Then draw vectors from each y-axis point to a corresponding x-axis point, and also from each x-axis point to a corresponding y-axis point, creating a set of crossing arrows. These vectors spread on both sides of the axes, with varied directions and lengths, illustrating the geometric idea of adding functions via corresponding point connections. The figure uses the axes as a framework and arrows as key elements.
The prompt above was compiled from the original drawing commands and is for reference only.