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Function Translations by cemccourseware

Function Translations by cemccourseware
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2019-02-13 02:15
FunctionTransformation
This example demonstrates the process of translating functions. Key mathematical concepts include functions, quadratic functions, and translations. Using GeoGebra commands such as Polygon, If, LaTeX, etc., it dynamically shows the effect of translating function graphs. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Polygon({(-11, -10.75), (-11, 10.75), (11, 10.75), (11, -10.75)}) → viewBox
  2. If(showQuadratic, x^(2), If[showSquareRoot, sqrt(x), 1 / x]) → preImageFunction
  3. LaTeX("f(x)=x^2") → quadraticBoxLabel
  4. If(showQuadratic, If[h ≟ 0, x^(2) + k, (x - h)^(2) + k], If[showSquareRoot, sqrt(x - h) + k, 1 / (x - h) + k]) → imageFunction
  5. LaTeX("f(x)=\sqrt{x}") → squareRootBoxLabel
  6. LaTeX("f(x)=\frac{1}{x}") → reciprocalBoxLabel
  7. Asymptote(preImageFunction) → asymptotePreImage
  8. Asymptote(imageFunction) → asymptoteImage
  9. If(showQuadratic, {-2, -1, 0, 1, 2}, If[showReciprocal, {-2, -1, -0.5, 0.5, 1, 2}, {0, 1, 4}]) → xValues
  10. Zip((A, preImageFunction(A)), A, xValues) → preImagePoints
  11. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  12. LaTeX(("\vphantom{-1}k=" * k)) → kLabel
  13. LaTeX(("\vphantom{-1}h=" * h)) → hLabel
  14. Zip((A, imageFunction(A)), A, Zip[B + h, B, xValues]) → imagePoints