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Linear Functions and Real-World Applications: Visualizing Price Relationships

Linear Functions and Real-World Applications: Visualizing Price Relationships
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2025-10-04 18:53
In collections Homogen lineare Funktionen
This example demonstrates how linear functions can model real-world price relationships. Key mathematical concepts include the definition of linear functions, the geometric meaning of slope and intercept, and how to visualize abstract relationships using coordinate systems. Construction points involve using GeoGebra commands to draw function graphs, setting axis proportions, adding data points, an

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {2, 4, 8, 4, 6, 7, 5, 3, 2, 3}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Circle(ziehM1, ziehZone) → ziehK1
  5. Circle(ziehM2, ziehZone) → ziehK2
  6. Circle(ziehM3, ziehZone) → ziehK3
  7. Circle(ziehM4, ziehZone) → ziehK4
  8. Circle(ziehM1, ziehZone) → ziehK5
  9. CountIf(m ∈ ziehK1, m, listCross) → anz31
  10. CountIf(m ∈ ziehK2, m, listCross) → anz32
  11. CountIf(m ∈ ziehK3, m, listCross) → anz33
  12. CountIf(m ∈ ziehK4, m, listCross) → anz34
  13. CountIf(m ∈ ziehK5, m, listCross) → anz35
  14. Polygon(check5LO, check5RO, check5RU, check5LU) → v2, e, f, g, h
  15. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  16. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  17. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  18. Segment(Tab1LO, Tab1RO) → tabO
  19. Segment(Tab1RU, Tab1LU) → tabU
  20. Segment(Tab1LU, Tab1LO) → tabL
  21. Segment(Tab1RO, Tab1RU) → tabR
  22. Midpoint(tabO) → Tab1MO
  23. Midpoint(tabU) → Tab1MU
  24. Segment(Tab1MO, Tab1MU) → tab1M
  25. Sequence(Tab1LO - (0, 0.3) + (0, (i * (y(Tab1LU) - y(Tab1LO) + 0.3) / 6)), i, 1, 5) → listAllTab1L
  26. Sequence(Tab1RO - (0, 0.3) + (0, (i * (y(Tab1RU) - y(Tab1LO) + 0.3) / 6)), i, 1, 5) → listAllTab1R
  27. Sequence(Segment[listAllTab1L(i), listAllTab1R(i)], i, 1, 5) → listAllTab1Strichs
  28. Textfield(input21) → inputBox21
  29. Textfield(input22) → inputBox22
  30. Textfield(input23) → inputBox23
  31. Textfield(input24) → inputBox24
  32. Segment(DiagramYO, DiagramYU) → DiagramY
  33. Segment(DiagramXL, DiagramXR) → DiagramX
  34. Corner(txtMaria3, 1) → Maria3LU
  35. Corner(txtMaria3, 2) → Maria3RU
  36. Corner(txtMaria3, 3) → Maria3RO
  37. Corner(txtMaria3, 4) → Maria3LO
  38. Segment(Maria3LU, Maria3RU) → maria3txt_{1}
  39. Segment(Maria3RU, Maria3RO) → maria3txt_{2}
  40. Segment(Maria3RO, Maria3LO) → maria3txt_{3}
  41. Segment(Maria3LO, Maria3O) → maria3txt_{4}
  42. Segment(Maria3O, Maria3H) → maria3txt_{5}
  43. Segment(Maria3H, Maria3U) → maria3txt_{6}
  44. Segment(Maria3U, Maria3LU) → maria3txt
  45. Polygon(Farb51_{1}, Farb51_{3}, Farb51, Farb51_{2}) → v1, a, b, c, d
  46. Textfield(input51) → inputBox51
  47. Textfield(input52) → inputBox52
  48. Corner(txtMaria6, 1) → marie6LU
  49. Corner(txtMaria6, 2) → marie6RU
  50. Corner(txtMaria6, 3) → marie6RO
  51. Corner(txtMaria6, 4) → marie6LO
  52. Segment(marie6LO, marie6O) → marie6Rand_{5}
  53. Segment(marie6O, marie6H) → marie6Rand_{6}
  54. Segment(marie6H, marie6U) → marie6Rand
  55. Segment(marie6U, marie6LU) → marie6Rand_{1}
  56. Segment(marie6LU, marie6RU) → marie6Rand_{2}
  57. Segment(marie6RU, marie6RO) → marie6Rand_{3}
  58. Segment(marie6RO, marie6LO) → marie6Rand_{4}
  59. Polygon(lupArea_{1}, lupArea_{2}, lupArea_{3}, lupArea_{4}, lupArea_{5}, lupArea) → luArea, c_5, d_5, g_2, h_2, i_2, j_2
  60. PointIn(luArea) → LupeL
  61. Circle(lupKreisM, 0.64) → lupKreis
  62. Polygon(Box7LO, Box7RO, Box7RU, Box7LU) → box7, a_1, b_1, c_1, d_1
  63. Textfield(input53f) → inputBox53
  64. Polygon(Farb51_{4}, Farb51_{5}, Farb51_{6}, Farb51_{7}) → v1_{1}, a_{2}, b_{2}, c_{2}, d_{2}
  65. Polygon(Box7LO_{1}, Box7RO_{1}, Box7RU_{1}, Box7LU_{1}) → box7_{1}, a_{3}, b_{3}, c_{3}, d_{3}
  66. Segment(ziehM1, GeradeO) → Gerade
  67. Segment(Tab1LO_{1}, Tab1RO_{1}) → tabO_{1}
  68. Segment(Tab1RU_{1}, Tab1LU_{1}) → tabU_{1}
  69. Segment(Tab1LU_{1}, Tab1LO_{1}) → tabL_{1}
  70. Segment(Tab1RO_{1}, Tab1RU_{1}) → tabR_{1}
  71. Sequence(Tab1LO_{1} + (0, (i * (y(Tab1LU_{1}) - y(Tab1LO_{1})) / 6)), i, 1, 5) → listAllTab1L_{1}
  72. Sequence(Tab1RO_{1} + (0, (i * (y(Tab1RU_{1}) - y(Tab1LO_{1})) / 6)), i, 1, 5) → listAllTab1R_{1}
  73. Segment(DiagramXL_{1}, DiagramXR_{1}) → DiagramX_{1}
  74. Segment(DiagramYO_{1}, DiagramYU_{1}) → DiagramY_{1}
  75. Segment(GeradeU_{1}, GeradeO_{1}) → Gerade_{1}
  76. Polygon(whiteSquareLO, whiteSquareRO, whiteSquareRU, whiteSquareLU) → v3, a_4, b_4, c_4, d_4
  77. Sequence(If[i ≠ 1, Segment[DiagramXL_{1} + (0.4, 0) + ((i * (x(DiagramXR_{1}) - 0.4 - (x(DiagramXL_{1}) + 0.4)) / 8), 0.12), DiagramXL_{1} + (0.4, 0) + ((i * (x(DiagramXR_{1}) - 0.4 - (x(DiagramXL_{1}) + 0.4)) / 8), -0.12)]], i, 0, 8) → listStricheX_{1}
  78. Sequence(If[i ≠ 1, Segment[DiagramYU_{1} + (0, 0.4) + (0.12, (i * (y(DiagramYO_{1}) - 0.4 - (y(DiagramYU_{1}) + 0.4)) / 6)), DiagramYU_{1} + (0, 0.4) + (-0.12, (i * (y(DiagramYO_{1}) - 0.4 - (y(DiagramYU_{1}) + 0.4)) / 6))]], i, 0, 6) → listStricheY_{1}
  79. Polygon(Tab1LO, listAllTab1L(1), listAllTab1R(1), Tab1RO) → q1, tab1lo, l, m, tab1ro
  80. Polygon(listAllTab1L(1), listAllTab1L(2), listAllTab1R(2), listAllTab1R(1)) → q2, n, p, q, r
  81. Polygon(listAllTab1L(2), listAllTab1L(3), listAllTab1R(3), listAllTab1R(2)) → q3, s, t, f_1, g_1
  82. Polygon(listAllTab1L(3), listAllTab1L(4), listAllTab1R(4), listAllTab1R(3)) → q4, h_1, i_1, j_1, k_1
  83. Polygon(listAllTab1L(4), listAllTab1L(5), listAllTab1R(5), listAllTab1R(4)) → q5, l_1, m_1, n_1, p_1
  84. Polygon(listAllTab1L(5), Tab1LU, Tab1RU, listAllTab1R(5)) → q6, q_1, tab1lu, tab1ru, r_1
  85. Sequence(If[i ≥ 1, Segment[DiagramYU + (0, 0) + (0.12, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0)) / 4)), DiagramYU + (0, 0) + (-0.12, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0)) / 4))]], i, 0, 4) → listStricheY
  86. Sequence(Segment[DiagramXL + (0, (i * (y(DiagramYO - 0.4) - y(DiagramXL)) / 4)), DiagramXR + (0, (i * (y(DiagramYO - 0.4) - y(DiagramXL)) / 4))], i, 1, 4) → l2
  87. Segment(DiagramXL_{2}, DiagramXR_{2}) → DiagramX_{2}
  88. Segment(DiagramYO_{2}, DiagramYU_{2}) → DiagramY_{2}
  89. Sequence(If[i ≠ 1, Segment[DiagramXL_{1} + (0.4, 0) + ((i * (x(DiagramXR_{1}) - 0.4 - (x(DiagramXL_{1}) + 0.4)) / 8), y(DiagramYO_{1}) - y(DiagramXL_{1})), DiagramXL_{1} + (0.4, 0) + ((i * (x(DiagramXR_{1}) - 0.4 - (x(DiagramXL_{1}) + 0.4)) / 8), y(DiagramYU_{1}) - y(DiagramXL_{1}))]], i, 0, 8) → l1_{1}
  90. Segment(DiagramYO_{5}, DiagramYU_{5}) → DiagramY_{3}
  91. Sequence(If[i ≠ 1, Segment[DiagramYU_{1} + (0, 0.4) + (x(DiagramXR_{1}) - x(DiagramYU_{1}), (i * (y(DiagramYO_{1}) - 0.4 - (y(DiagramYU_{1}) + 0.4)) / 6)), DiagramYU_{1} + (0, 0.4) + (x(DiagramXL_{1}) - x(DiagramYU_{1}), (i * (y(DiagramYO_{1}) - 0.4 - (y(DiagramYU_{1}) + 0.4)) / 6))]], i, 0, 6) → l2_{1}
  92. Segment(mark03X1_{2}, mark03X1_{3}) → mark03X1
  93. Segment(mark03X2_{3}, mark03X2_{2}) → mark03X2
  94. Sequence(Segment[DiagramXL + (i * (x(DiagramXR - 0.4) - x(DiagramXL), 0) / 6), DiagramYO + ((i * (x(DiagramXR - 0.4) - x(DiagramXL)) / 6), 0)], i, 1, 6) → l1
  95. Sequence(If[i > 0, Segment[DiagramXL + (0, 0) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0)) / 6), 0.12), DiagramXL + (0, 0) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0)) / 6), -0.12)]], i, 0, 6) → listStricheX
  96. Segment(cross1 + ((-sizeCrossCorrect), sizeCrossCorrect), cross1 - ((-sizeCrossCorrect), sizeCrossCorrect)) → cross1Correct1
  97. Segment(cross1 + ((-sizeCrossCorrect), (-sizeCrossCorrect)), cross1 + (sizeCrossCorrect, sizeCrossCorrect)) → cross1Correct2
  98. Segment(cross2 + ((-sizeCrossCorrect), sizeCrossCorrect), cross2 - ((-sizeCrossCorrect), sizeCrossCorrect)) → cross2Correct1
  99. Segment(cross2 + ((-sizeCrossCorrect), (-sizeCrossCorrect)), cross2 + (sizeCrossCorrect, sizeCrossCorrect)) → cross2Correct2
  100. Segment(cross3 + ((-sizeCrossCorrect), sizeCrossCorrect), cross3 - ((-sizeCrossCorrect), sizeCrossCorrect)) → cross3Correct1
  101. Segment(cross3 + ((-sizeCrossCorrect), (-sizeCrossCorrect)), cross3 + (sizeCrossCorrect, sizeCrossCorrect)) → cross3Correct2
  102. Segment(cross4 + ((-sizeCrossCorrect), sizeCrossCorrect), cross4 - ((-sizeCrossCorrect), sizeCrossCorrect)) → cross4Correct1
  103. Segment(cross4 + ((-sizeCrossCorrect), (-sizeCrossCorrect)), cross4 + (sizeCrossCorrect, sizeCrossCorrect)) → cross4Correct2