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Calculate Function Values

Calculate Function Values
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2025-07-31 17:05
In collections Einführung Funktionsbegriff
This example demonstrates how to calculate the output values of a function for different inputs. Key math concepts include the definition of functions, calculation of function values, and the conversion between different function representations (e.g., function equations, tables, graphs). GeoGebra commands and objects like Textfield, Shuffle, Flatten, Sequence, If, Element, Join, Translate, Replac

GeoGebra Commands & Parameters

  1. Textfield(input) → inputBox
  2. Shuffle(1…7) → OrderFuncLevel1, {1, 2, 3, 5, 4, 7, 6}
  3. Flatten(Sequence[OrderFuncLevel1, k, 1, 30]) → Level1Func
  4. Flatten(Sequence[OrderFuncLevel1, k, 1, 30]) → Level2Func
  5. Flatten(Sequence[OrderFuncLevel1, k, 1, 30]) → Level3Func
  6. Sequence(k, k, -20, 20, 1) → PossibleValuesLevel2
  7. Sequence(RandomElement[PossibleValuesLevel1], k, 1, 200) → ValuesLevel1, {-3, -4, -6, -10, -8, -5, -3, 10, 5, 2, 7, 6, -10, 5, 5, 0, 4, 9, 8, -9, 7, -3, 2, 0, -4, 5, 7, 9, 0, 8, 4, 10, 0, 2, -7, -1, -7, 3, -8, -9, -9, 2, 6, 0, 5, 7, 0, -2, 7, 7, 5, -7, 8, 2, 4, 9, -1, -1, -9, 4, 10, 9, 6, -4, -1, -9, 7, 3, 0, 8, -9, 10, -5, -4, -3, -9, -2, -8, -1, 2, -10, -5, 9, 6, -3, -3, -4, 0, 7, -9, -2, -7, -9, -2, 9, 2, 8, -9, -5, 0, -4, -6, 1, -9, 0, -8, 1, -10, -3, -10, -6, 9, 2, -8, 8, 7, -3, 1, 9, -4, 0, 10, -2, 9, -10, 8, -4, -4, -10, -1, -1, -7, 6, 1, -7, 3, -9, 5, 10, -7, 2, -8, 1, 6, -6, 6, 9, 10, -1, -7, -4, -2, 0, 7, 6, -6, 3, -6, -6, 7, 4, 4, 5, -10, 0, 6, 7, -3, 7, 5, 5, 2, 9, 1, -10, 0, 6, -9, -10, 5, -4, -10, -10, 5, 4, 7, 10, -6, -5, -7, 7, 6, -5, -9, -10, -10, 2, -2, 7, 9}
  8. Sequence(RandomElement[PossibleValuesLevel2], k, 1, 200) → ValuesLevel2, {-20, 12, -4, 8, 3, -10, 14, 0, 16, 5, 18, 12, -9, 1, -8, 20, -4, -13, 13, -4, 20, -19, -11, -12, 3, 5, 9, 18, -2, -20, 11, -3, 13, -13, -20, 1, 7, 14, 18, 19, -17, 4, 16, 19, 15, 4, -16, -20, 5, -18, -12, 7, -11, 6, 7, 6, 8, 12, 4, 11, -6, -10, -17, 20, 17, 8, 10, 7, -5, -20, -4, 10, 9, -20, 6, -9, 10, -4, 9, 16, -14, -8, 11, -11, -7, -6, -15, -17, -12, 6, 2, 15, 9, 16, -2, 0, 20, 12, 12, -13, 20, 13, -6, -14, -18, -6, 5, -4, -16, 10, -15, 1, 19, 14, -3, 2, 10, -19, 17, -10, -7, 8, 1, 2, -5, -11, -20, 8, -13, 1, 18, -13, 7, -3, 20, 2, 7, 7, -19, 11, 9, -1, 3, 4, 20, 1, -10, -10, 4, 5, -10, 14, 20, -15, -14, -3, -13, 4, -6, 11, 6, -17, -4, -16, -1, -17, -17, -11, 3, 20, -7, 9, -2, -2, 3, 12, 18, 3, 1, -6, 7, -15, -17, 6, -20, -1, -11, 7, 9, 2, 9, 1, 8, -2, 6, 17, 1, -13, 6, 18}
  9. Sequence(RandomElement[Remove[PossibleValuesLevel3, RemoveListLevel3(Level3Func(k))]], k, 1, 200) → ValuesLevel3, {12, 13, -10, -4, 4, -13, -9, -1, 0, -11, 13, -7, 6, 14, -3, -4, 11, -15, 13, 6, -3, -15, -3, -11, -13, 7, 15, -12, -4, 15, -8, -4, 14, -1, -15, 7, -2, -6, 1, -7, -6, 6, 6, 11, -12, -9, 12, 15, 2, 6, 10, 12, -12, -5, -1, 11, -7, 9, -4, -7, -10, -7, -10, -5, -5, -14, -14, 0, 13, 9, -12, -12, 4, -4, -9, -8, 13, 9, 12, 8, 13, -5, 7, 11, -11, -10, -10, 1, -3, -10, -15, 5, -5, -10, -1, 14, 8, 6, -15, 2, 9, 9, -11, -8, -12, -10, -6, 13, -9, 4, -10, 5, -7, -4, -6, -13, 9, 8, 3, 7, 8, 2, 2, 5, -1, -10, 6, -7, -4, -6, 10, -1, -2, -8, -1, 2, 2, 1, 8, 9, 9, -4, -6, 11, 10, -4, -14, 3, -9, -8, 14, 1, 6, -2, -10, -6, -7, 12, -14, -6, -5, -4, 10, -9, -1, -6, -1, -12, -9, -10, 0, -8, 5, -5, 6, -13, 5, 14, -3, 9, 9, 3, 9, -14, -4, -15, -15, 11, 2, 10, -9, 4, 12, 11, 15, -14, -1, -5, 3, -10}
  10. If(level ≟ 1, value1, level ≟ 2, value2, value3) → value
  11. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {6, 8, 4, 3, 9, 10, 2, 7, 4, 9}
  12. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  13. 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
  14. 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
  15. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  16. Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
  17. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  18. Translate(imgChilliRot1, Vector[(2 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
  19. Shuffle(1…8) → OrderFuncLevel2, {7, 8, 1, 2, 3, 4, 6, 5}
  20. Shuffle(1…7) → OrderFuncLevel3, {4, 5, 2, 1, 7, 6, 3}
  21. ReplaceAll(ReplaceAll[txtFunc1, "x", If[value < 0, (("(\\(" * value) * "\\))"), ("" * value)]], "\:", " \\cdot ") → replacedFunc1
  22. ReplaceAll(If[level ≟ 1, txtFunc1, level ≟ 2, txtFunc2, txtFunc3], "x", (("\\textcolor{" * If[showHint, "db6114", "black"]) * "}{x}")) → txtFunc
  23. ReplaceAll(ReplaceAll[txtFunc2, "x", If[value < 0, (("(\\(" * value) * "\\))"), ("" * value)]], "\:", " \\cdot ") → replacedFunc2
  24. ReplaceAll(ReplaceAll[txtFunc3, "x", If[value < 0, (("(\\(" * value) * "\\))"), ("" * value)]], "\:", " \\cdot ") → replacedFunc3
  25. NumberSeparationCommaText((value * "")) → txtValue
  26. If(level ≟ 1, replacedFunc1, level ≟ 2, replacedFunc2, replacedFunc3) → replacedFunc
  27. Defined(IndexOf["/", Split[Text[inputBox], {""}]]) → isFraction
  28. Split(If[input < 0, Take[Text[inputBox], 3, Length[Text[inputBox]] - 1], Text[inputBox]], {"/"}) → FractionComponents
  29. ParseToNumber(FractionComponents(1)) → inputNumerator
  30. ParseToNumber(FractionComponents(2)) → inputDenominator
  31. If(isFraction ∧ correctSigns, GCD[inputNumerator, inputDenominator] ≟ 1, true) → fractionSimplified