MathPlotAI Logo MathPlotAI

GeoGebra Math Example: Multi-Function and Geometric Construction

GeoGebra Math Example: Multi-Function and Geometric Construction
Loading the math board and drawing, please wait…
2023-02-15 22:10
FunctionTrigonometryGeometric Construction
In collections Function Arts
This example demonstrates the relationship between multiple function graphs and geometric constructions using GeoGebra. Key mathematical concepts include power functions, trigonometric functions, conditional probability, and differential calculus. Construction involves objects like A, B, f, g, h and parameters f₁, g₁, etc. Suitable for high school students learning function transformations and geometric intuition.

GeoGebra Commands & Parameters

  1. (-5.872, 0.118)
  2. (6.1, 0.11)
  3. f(x) = ((x + 3) * 0.429) + 0.7
  4. g(x) = If[-3 ≤ x ≤ 6, f(x)]
  5. h(x) = (0.13 * (x + 4.5)^(2)) + 0.4
  6. p(x) = If[-4.5 ≤ x ≤ -3, h(x)]
  7. q(x) = (0.5 * (x + 4.5)^(2)) + 0.4
  8. r(x) = If[-5.6 ≤ x ≤ -4.5, q(x)]
  9. s(x) = (3.8 * (x + 5.4)^(2)) + 0.87
  10. f_{1}(x) = (4.9 * sin(x + 6.55)) - 1.7
  11. g_{1}(x) = If[-5.83 ≤ x ≤ -5.4, f_{1}(x)]
  12. h_{1}(x) = (1.5 * (x + 5.4)) + 2.8
  13. p_{1}(x) = If[-5.4 ≤ x ≤ -4.4, h_{1}(x)]
  14. q_{1}(x) = (3 * (x + 4.6)) + 3.6
  15. r_{1}(x) = If[-4.6 ≤ x ≤ -4.36, q_{1}(x)]
  16. s_{1}(x) = (19 * (x + 4.4)^(2)) + 2.7
  17. t_{1}(x) = If[-4.615 ≤ x ≤ -4.4, s_{1}(x)]
  18. f_{2}(x) = (0.49 * (x + 3.4)^(2)) + 2.2
  19. g_{2}(x) = If[-4.4 ≤ x ≤ -3.4, f_{2}(x)]
  20. h_{2}(x) = (0.268 * (x + 3)) + 2.2
  21. p_{2}(x) = If[-3 ≤ x ≤ 6, h_{2}(x)]
  22. q_{2}(x) = (0 * (x + 3.4)) + 2.2
  23. r_{2}(x) = If[-3.4 ≤ x ≤ -3, q_{2}(x)]
  24. s_{2}(x) = (2.6 * (x + 4.2)) + 3.4
  25. t(x) = If[-5.81 ≤ x ≤ -5.5, s(x)]
  26. f_{3}(x) = (2.6 * (x + 3.42)) + 3.4
  27. g_{3}(x) = If[-3.43 ≤ x ≤ -2.94, f_{3}(x)]
  28. h_{3}(x) = (0 * (x + 4.2)) + 3.38
  29. p_{3}(x) = If[-4.2 ≤ x ≤ -3.4, h_{3}(x)]
  30. q_{3}(x) = (0 * (x + 3)) + 6.54
  31. r_{3}(x) = If[-3 ≤ x ≤ -2.2, q_{3}(x)]
  32. s_{3}(x) = (16 * (x + 2.3)) + 5.1
  33. t_{3}(x) = If[-2.3 ≤ x ≤ -2.21, s_{3}(x)]
  34. f_{4}(x) = (16 * (x + 3)) + 3.4
  35. g_{4}(x) = If[-3 ≤ x ≤ -2.92, f_{4}(x)]
  36. h_{4}(x) = (0 * (x + 3)) + 3.4
  37. p_{4}(x) = If[-3 ≤ x ≤ -2.2, h_{4}(x)]
  38. q_{4}(x) = (2.8 * (x + 2.27)) + 5.1
  39. r_{4}(x) = If[-2.3 ≤ x ≤ -1.76, q_{4}(x)]
  40. s_{4}(x) = (2.6 * (x + 2.2)) + 3.4
  41. f_{5}(x) = (0 * (x + 1.8)) + 6.57
  42. g_{5}(x) = If[-1.76 ≤ x ≤ -1, f_{5}(x)]
  43. h_{5}(x) = (2.6 * (x + 2.1)) + 3.4
  44. p_{5}(x) = If[-2.1 ≤ x ≤ -0.9, h_{5}(x)]
  45. q_{5}(x) = (2.6 * (x + 1.38)) + 3.4
  46. r_{5}(x) = If[-1.38 ≤ x ≤ -0.18, q_{5}(x)]
  47. s_{5}(x) = (0 * (x + 1.2)) + 3.4
  48. t_{5}(x) = If[-2.1 ≤ x ≤ -1.4, s_{5}(x)]
  49. f_{6}(x) = (0 * (x + 0.9)) + 6.57
  50. h_{6}(x) = (2.7 * (x + 1.2)) + 3.4
  51. p_{6}(x) = If[-1.2 ≤ x ≤ -0.05, h_{6}(x)]
  52. g_{6}(x) = If[-0.9 ≤ x ≤ -0.16, f_{6}(x)]
  53. q_{6}(x) = (2.6 * (x + 0.45)) + 3.4
  54. r_{6}(x) = If[-0.45 ≤ x ≤ 0.04, q_{6}(x)]
  55. s_{6}(x) = (2.6 * (x - 04)) + 15
  56. t_{2}(x) = If[-4.2 ≤ x ≤ -3, s_{2}(x)]
  57. t_{6}(x) = If[0.4 ≤ x ≤ 0.75, s_{6}(x)]
  58. f_{7}(x) = (-24 * (x - 0.15)) + 3.3
  59. g_{7}(x) = If[0.09 ≤ x ≤ 0.147, f_{7}(x)]
  60. h_{7}(x) = (-22 * (x - 1))

AI Drawing Prompt Reference

Draw a graph featuring multiple function plots, showcasing the relationship between power functions, trigonometric functions, and geometric constructions. Key elements include piecewise-defined functions f, g, h and their transformations, along with geometric curves controlled by conditional probability. Start by plotting the base function curves, then add conditional geometric objects, and finally overlay trigonometric function images to illustrate function transformations and geometric intuition.
The prompt above was compiled from the original drawing commands and is for reference only.