Collection of 35 Predefined Functions

Collection of 35 Predefined Functions
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2013-11-08 18:38
This example demonstrates 35 predefined 3D functions, involving functions, surfaces, and parametric equations. Using GeoGebra commands such as If, Sequence, Vector, etc., you can dynamically adjust parameters to observe changes in the function graphs. Suitable for high school and above students and teachers.

GeoGebra Commands & Parameters

  1. If(jg, t, x_{min} + x_{max} - t) → tj
  2. Corner(3) → Eckpunkt3
  3. Corner(2) → Eckpunkt2
  4. If(c, β, y(C - Eckpunkt2) / dEy * c_{Move}) → β1
  5. Corner(1) → Eckpunkt1
  6. If(c, α, x(C - Eckpunkt1) / dEx * c_{Move}) → α1
  7. If(x ≟ 0, 1, sin(x) / x) → sinc
  8. Element(lFr, Funktion) → f
  9. If(a ∧ bP, tj) → tt2
  10. If(a ∧ (¬bP), tj) → tt1
  11. Mod(β1, 6.283) → β2
  12. Mod(α1, 6.283) → α2
  13. Sequence(a11 * Element[zWX1, i] + a12 * Element[zWY1, i] + a13 * Element[zWZ1, i], i, 1, 4) → zWX1'
  14. Element(zWW_0, 3) → zW_2
  15. Element(zWW_0, 4) → zW_1
  16. Element(zWW_0, 2) → zW_3
  17. Polygon(Eckpunkt1, Eck11, Eck12, (x(Eckpunkt1), y(Eck12))) → Vieleck2, eckpunkt1, eck11, eck12, a_1
  18. Sequence(Segment[Element[zl10, i], Element[zl10, i + 1]], i, 1, 7) → BoxStr
  19. Vector(Element[zl10, 4], Element[zl10, 1]) → zVectx
  20. Vector(Element[zl10, 4], Element[zl10, 3]) → zVecty
  21. Vector(Element[zl10, 4], Element[zl10, 5]) → zVectz
  22. Polygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12) → Vieleck1, eck11_1, eckpunkt2, eckpunkt3, eck12_1
  23. Element(zTT, zW_1) → zY1
  24. Element(zTT, zW_2) → zY2
  25. Element(zTT, zW_3) → zY3
  26. Polygon(zTT) → zTTPoly, , , ,
  27. Element(zl10, zW_1) → zlN11
  28. Element(zl10, 9 - zW_1) → zlN111
  29. Element(zl10, zW_2) → zlN22
  30. Element(zl10, 9 - zW_2) → zlN222
  31. Element(zl10, zW_3) → zlN33
  32. Element(zWW_0, 1) → zW_4
  33. Element(zl10, zW_4) → zlN44
  34. Polygon({zlN11, zlN22, zlN222, zlN111}) → Vgrund01, , , ,
  35. Polygon(Sequence[Element[zl10, i], i, 1, 4]) → Vgrund000, , , ,
  36. Element(zl10, 7) → P_R
  37. Element(zl10, 8) → P_L
  38. Polygon({Element[zl10, 1], Element[zl10, 2], Element[zl10, 7], Element[zl10, 8]}) → Vvrd0, , , ,
  39. Segment(P_R, P_L) → StrRL
  40. Polygon(Sequence[Element[zl10, i], i, 9, 12]) → zlPoly, n, r, s, c_1
  41. Ray(B, Element[zl10, 13]) → Strx
  42. Ray(B, Element[zl10, 14]) → Stry
  43. Ray(B, Element[zl10, 15]) → Strz
  44. Textfield(x_{min}) → inputBox1
  45. Textfield(x_{max}) → inputBox4
  46. Textfield(v_{Animation}) → inputBox8
  47. Textfield(Step) → inputBox7
  48. Textfield(N) → inputBox9
  49. If(b, t, t0) → Rot
  50. If(b, exp(t), sin(π * t0)) → Grün
  51. If(b, ℯ^(-t), 1 - (t0 - 0.5)^(2)) → Blau
  52. Textfield(t) → inputBox10
  53. Textfield(Th) → inputBox3
  54. Textfield(y_{min}) → inputBox5
  55. Textfield(z_{min}) → inputBox6
  56. Textfield(z_{max}) → inputBox11
  57. Textfield(y_{max}) → inputBox12
  58. Textfield(g00r) → inputBox2
  59. Segment((x_{min}, 0), (x_{max}, 0)) → Sx
  60. Segment((0, y_{min}), (0, y_{max})) → Sy
  61. Point(Sx) → Ax
  62. Point(Sy) → Ay
  63. Locus(A', y0) → locu
  64. Locus(A, y0) → locy
  65. Locus(A', x0) → locv
  66. Textfield(Funktion) → inputBox13
  67. Locus(M5_{1}, Ay) → M6_{1}
  68. Locus(M5_{2}, Ay) → M6_{2}
  69. Locus(M5_{3}, Ay) → M6_{3}
  70. Locus(M5_{4}, Ay) → M6_{4}
  71. Locus(M5_{5}, Ay) → M6_{5}
  72. Locus(M5_{6}, Ay) → M6_{6}
  73. Locus(M5_{7}, Ay) → M6_{7}
  74. Locus(M5_{8}, Ay) → M6_{8}
  75. Locus(M5_{9}, Ay) → M6_{9}
  76. Locus(M5_{10}, Ay) → M6_{10}
  77. Locus(M5_{11}, Ay) → M6_{11}
  78. Locus(M5_{12}, Ay) → M6_{12}
  79. Locus(M5_{13}, Ay) → M6_{13}
  80. Locus(M5_{14}, Ay) → M6_{14}
  81. Locus(M5_{15}, Ay) → M6_{15}
  82. Locus(M5_{16}, Ay) → M6_{16}
  83. Locus(M5_{17}, Ay) → M6_{17}
  84. Locus(M5_{18}, Ay) → M6_{18}
  85. Locus(M5_{19}, Ay) → M6_{19}
  86. Locus(M5_{20}, Ay) → M6_{20}
  87. Locus(M5_{21}, Ay) → M6_{21}
  88. Locus(M5_{22}, Ay) → M6_{22}
  89. Locus(M5_{23}, Ay) → M6_{23}
  90. Locus(M5_{24}, Ay) → M6_{24}
  91. Locus(M5_{25}, Ay) → M6_{25}
  92. Locus(M5_{26}, Ay) → M6_{26}
  93. Locus(M5_{27}, Ay) → M6_{27}
  94. Locus(M5_{28}, Ay) → M6_{28}
  95. Locus(M5_{29}, Ay) → M6_{29}
  96. Locus(M5_{30}, Ay) → M6_{30}
  97. Locus(M5_{31}, Ay) → M6_{31}
  98. Locus(M5_{32}, Ay) → M6_{32}
  99. Locus(M5_{33}, Ay) → M6_{33}
  100. Locus(M5_{34}, Ay) → M6_{34}
  101. Locus(M5_{35}, Ay) → M6_{35}
  102. Locus(M5_{36}, Ay) → M6_{36}
  103. Locus(M5_{37}, Ay) → M6_{37}
  104. Locus(M5_{38}, Ay) → M6_{38}
  105. Locus(M5_{39}, Ay) → M6_{39}
  106. Locus(M5_{40}, Ay) → M6_{40}
  107. Locus(M5_{41}, Ay) → M6_{41}
  108. Locus(M5_{42}, Ay) → M6_{42}
  109. Locus(M5_{43}, Ay) → M6_{43}
  110. Locus(M5_{44}, Ay) → M6_{44}
  111. Locus(M5_{45}, Ay) → M6_{45}
  112. Locus(M5_{46}, Ay) → M6_{46}
  113. Locus(M5_{47}, Ay) → M6_{47}
  114. Locus(M5_{48}, Ay) → M6_{48}
  115. Locus(M5_{49}, Ay) → M6_{49}
  116. Locus(M5_{50}, Ay) → M6_{50}
  117. Locus(M5_{51}, Ay) → M6_{51}
  118. Locus(M5_{52}, Ay) → M6_{52}
  119. Locus(M5_{53}, Ay) → M6_{53}
  120. Locus(M5_{54}, Ay) → M6_{54}
  121. Locus(M5_{55}, Ay) → M6_{55}
  122. Locus(M5_{56}, Ay) → M6_{56}
  123. Locus(M5_{57}, Ay) → M6_{57}
  124. Locus(M5_{58}, Ay) → M6_{58}
  125. Locus(M5_{59}, Ay) → M6_{59}
  126. Locus(M5_{60}, Ay) → M6_{60}
  127. Locus(M5_{61}, Ay) → M6_{61}
  128. Locus(M5_{62}, Ay) → M6_{62}
  129. Locus(M5_{63}, Ay) → M6_{63}
  130. Locus(M5_{64}, Ay) → M6_{64}
  131. Locus(M5_{65}, Ay) → M6_{65}
  132. Locus(M5_{66}, Ay) → M6_{66}
  133. Locus(M5_{67}, Ay) → M6_{67}
  134. Locus(M5_{68}, Ay) → M6_{68}
  135. Locus(M5_{69}, Ay) → M6_{69}
  136. Locus(M5_{70}, Ay) → M6_{70}
  137. Locus(M5_{71}, Ay) → M6_{71}
  138. Locus(M5_{72}, Ay) → M6_{72}
  139. Locus(M5_{73}, Ay) → M6_{73}
  140. Locus(M5_{74}, Ay) → M6_{74}
  141. Locus(M5_{75}, Ay) → M6_{75}
  142. Locus(M5_{76}, Ay) → M6_{76}
  143. Locus(M5_{77}, Ay) → M6_{77}
  144. Locus(M5_{78}, Ay) → M6_{78}
  145. Locus(M5_{79}, Ay) → M6_{79}
  146. Locus(M5_{80}, Ay) → M6_{80}
  147. Locus(M5_{81}, Ay) → M6_{81}
  148. Locus(M5_{82}, Ay) → M6_{82}
  149. Locus(M5_{83}, Ay) → M6_{83}
  150. Locus(M5_{84}, Ay) → M6_{84}
  151. Locus(M5_{85}, Ay) → M6_{85}
  152. Locus(M5_{86}, Ay) → M6_{86}
  153. Locus(M5_{87}, Ay) → M6_{87}
  154. Locus(M5_{88}, Ay) → M6_{88}
  155. Locus(M5_{89}, Ay) → M6_{89}
  156. Locus(M5_{90}, Ay) → M6_{90}
  157. Locus(M5_{91}, Ay) → M6_{91}
  158. Locus(M5_{92}, Ay) → M6_{92}
  159. Locus(M5_{93}, Ay) → M6_{93}
  160. Locus(M5_{94}, Ay) → M6_{94}
  161. Locus(M5_{95}, Ay) → M6_{95}
  162. Locus(M5_{96}, Ay) → M6_{96}
  163. Locus(M5_{97}, Ay) → M6_{97}
  164. Locus(M5_{98}, Ay) → M6_{98}
  165. Locus(M5_{99}, Ay) → M6_{99}
  166. Locus(M5_{100}, Ay) → M6_{100}
  167. Locus(M5_{101}, Ay) → M6_{101}

AI Drawing Prompt Reference

Draw a collection of 35 predefined 3D functions, including functions, surfaces, and parametric equations. Use sliders to adjust parameters and observe changes in the function graphs. Start with basic functions like sine, then add parametric equations and surfaces, and finally dynamically adjust parameters using sliders to observe the changes in the graphics.
The prompt above was compiled from the original drawing commands and is for reference only.