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Translations of Absolute Value Functions

Translations of Absolute Value Functions
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2019-03-05 02:01
FunctionTransformationGraphing
This example demonstrates the translations of absolute value functions. Key mathematical concepts include function transformations and translations. Using GeoGebra commands such as Sequence, If, and Textfield, users can observe the changes in the function graph visually. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. UnicodeToLetter(8226) → bullet
  2. Random(-3, 3) → cVal
  3. Random(1, 10) → aValIndx
  4. Element(aValOptions, aValIndx) → aVal
  5. Sequence((12, i), i, 21, 0, -3.8) → boxAnchorRight
  6. UnicodeToLetter(10007) → xmark
  7. UnicodeToLetter(10003) → cmark
  8. If(F11, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G11
  9. If(F12, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G12
  10. If(F13, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G13
  11. If(F14, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G14
  12. If(F15, correct, incorrect) → G15
  13. If(F16, correct, incorrect) → G16
  14. LaTeX("\text{Vertical translation\hphantom{00000000} by a factor of }") → E14
  15. LaTeX("\text{Horizontal translation\hphantom{00000000} by a factor of }") → E13
  16. LaTeX("\text{Vertical\hphantom{00000000000000} by a factor of }") → E12
  17. LaTeX("\text{Reflection in the \(x\)-axis?}") → E15
  18. LaTeX("\text{Horizontal stretch?}") → E11
  19. LaTeX("\text{Reflection in the \(y\)-axis?}") → E16
  20. LaTeX(Expand[f]) → fTxt
  21. Textfield(F4) → E4
  22. Textfield(F5) → E5
  23. Textfield(F6) → E6
  24. Textfield(F7) → E7
  25. Sequence("\phantom{\dfrac{1}{2}vertical compression000000000}", i, 1, 6) → spacersDropDown
  26. LaTeX(If[aVal < 0, (bullet * " Reflection in the \(x\)-axis. \\"), ""]) → fbReflection
  27. LaTeX(If[abs(aVal) ≟ 1, "", If[abs(aVal) > 1, (((bullet * " Vertical stretch by a factor of ") * abs(aVal)) * ". \\"), (((bullet * " Vertical compression by a factor of ") * abs(1 / aVal)) * ". \\")]]) → fbvStretch
  28. LaTeX(If[abs(cVal) ≟ 0, "", (((((((bullet * " Horizontal translation ") * If[cVal < 0, "left", "right"]) * " by ") * abs(cVal)) * " unit") * If[abs(cVal) > 1, "s", ""]) * ".\\")]) → fbhTrans
  29. LaTeX(If[abs(dVal) ≟ 0, "", (((((((bullet * " Vertical translation ") * If[dVal < 0, "down", "up"]) * " by ") * abs(dVal)) * " unit") * If[abs(dVal) > 1, "s", ""]) * ".\\")]) → fbvTrans
  30. If(B6, If[SelectedIndex[hShiftLst] ≟ 1, G6, If[SelectedIndex[hShiftLst] ≟ 2, (-G6), 1]], 0) → userC
  31. If(B7, If[SelectedIndex[vShiftLst] ≟ 1, G7, If[SelectedIndex[vShiftLst] ≟ 2, (-G7), 1]], 0) → userD
  32. Polygon({(left, top), (right, top), (right, bottom), (left, bottom)}) → viewbox
  33. Segment(Element[legendAnchors, 1], Element[legendAnchors, 1] + (3, 0)) → legendF
  34. Segment(Element[legendAnchors, 2], Element[legendAnchors, 2] + (3, 0)) → legendH
  35. TableText({A2:A7, spacersDropDown, C2:C7}, "vr") → tblQuestions
  36. LaTeX(((((("\text{One possible solution is given below:\\" * fbReflection) * fbvStretch) * fbhTrans) * fbvTrans) * "}")) → fbComplete
  37. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  38. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewboxCover