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Horizontal and Vertical Translations of Exponential Functions

Horizontal and Vertical Translations of Exponential Functions
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2019-03-19 22:47
FunctionCoordinate GeometryTransformationGraphing
This example demonstrates horizontal and vertical translations of exponential functions. Key mathematical concepts include function transformations and translation transformations. Using GeoGebra commands such as Sequence, Segment, and If, the example dynamically shows the effect of translating function graphs. Suitable for high school mathematics education, helping students understand the basic principles of function graph transformations.

GeoGebra Commands & Parameters

  1. LaTeX(If[kValCorrect > 0, ("+" * kValCorrect), If[kValCorrect ≟ 0, "", ("-" * abs(kValCorrect))]]) → DisplayPlusK
  2. Random(-5, 5) → hValCorrect
  3. LaTeX(If[hValCorrect > 0, ("-" * hValCorrect), If[hValCorrect ≟ 0, "", ("+" * abs(hValCorrect))]]) → DisplayMinusH
  4. Shuffle({1 / 4, 1 / 3, 1 / 2, 2, 3, 4}) → potentialBaseValues
  5. Element(potentialBaseValues, 1) → base
  6. If(IsInteger[base], ("\vphantom{\frac{1}{1}}" * base), (("\left(" * FractionText[base]) * "\right)")) → baseDisplay
  7. Polygon({(-10.5, -10.5), (-10.5, 10.5), (10.5, 10.5), (10.5, -10.5)}) → viewBox
  8. LaTeX(((((("\vphantom{\frac{1}{1}}y=" * baseDisplay) * "^{x") * DisplayMinusH) * "}") * DisplayPlusK)) → translatedFuncLbl
  9. LaTeX(((MainInstruc * "\\") * SpecInstruc)) → InstructionsComplete
  10. LaTeX((UnicodeToLetter[10007] * "\text{ Incorrect}")) → incorrect
  11. LaTeX((UnicodeToLetter[10003] * "\text{ Correct}")) → correct
  12. LaTeX(If[hValUser > 0, ("-" * hValUser), If[hValUser ≟ 0, "", ("+" * abs(hValUser))]]) → DisplayUserMinusH
  13. LaTeX(If[kValUser > 0, ("+" * kValUser), If[kValUser ≟ 0, "", ("-" * abs(kValUser))]]) → DisplayUserPlusK
  14. LaTeX(((((baseDisplay * "^{x ") * DisplayUserMinusH) * "} ") * DisplayUserPlusK)) → userFunctionTxt
  15. LaTeX(If[kValCorrect ≟ 0, "", (((("a vertical translation of " * abs(kValCorrect)) * " unit") * If[abs(kValCorrect) > 1, "s ", " "]) * If[kValCorrect < 0, "\\down", "\\up"])]) → fbVertical
  16. LaTeX(If[hValCorrect ≟ 0, "", ((((("a horizontal translation of " * abs(hValCorrect)) * " unit") * If[abs(hValCorrect) > 1, "s", ""]) * "\\to the") * If[hValCorrect > 0, " right", " left"])]) → fbHorizontal
  17. Sequence((11, i), i, 9, 1, -4) → legendAnchors
  18. Segment(Element[legendAnchors, 1], Element[legendAnchors, 1] + (3, 0)) → legend1
  19. Segment(Element[legendAnchors, 2], Element[legendAnchors, 2] + (3, 0)) → legend2
  20. LaTeX((((((((("\text{In order to transform \(" * parentFuncLbl) * "\) into \\\(") * translatedFuncLbl) * "\), we must apply \\") * fbHorizontal) * If[hAndv, ", and ", ""]) * fbVertical) * ".}")) → fbComplete