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Reciprocal of a Linear Function

Reciprocal of a Linear Function
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2019-05-24 19:51
FunctionCoordinate GeometrySlider AnimationGraphing
This example demonstrates how to graph and analyze the reciprocal of a linear function, including its asymptotes. Key math concepts involve linear functions, reciprocal functions, asymptotes, and analytical geometry. Construction highlights GeoGebra commands like Polygon, Union, LineToSlopeFormRHS, RemoveUndefined, UnicodeToLetter, LaTeX, Point, Line, Zip, TableText, etc. Suitable for high school students learning function transformations and analytical geometry.

GeoGebra Commands & Parameters

  1. Polygon({(left, top), (right, top), (right, bottom), (left, bottom)}) → viewbox
  2. Union(Sequence[i, i, -5, 5], Zip[xIntercept + A, A, fractions]) → allXvalues
  3. LineToSlopeFormRHS(f) → lineTxt
  4. RemoveUndefined(Zip[If[A ≥ minX ∧ A ≤ maxX, A], A, allXvalues]) → useableXvalues
  5. UnicodeToLetter(10007) → xmark
  6. UnicodeToLetter(10003) → cmark
  7. LaTeX("\text{The asymptotes of \(y=\dfrac{1}{g(x)}\) \\occur at the zeros of \(g(x)\). \\The invariant points occur\\when \(y=\pm 1\).}") → fbExplanation
  8. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  9. Point(Zip[(C, f(C)), C, useableXvalues]) → A
  10. Line((xIntercept, 0), yAxis) → vAsymptote
  11. Zip((A, f(A)), A, useableXvalues) → useablePoints
  12. LaTeX("B") → lblB
  13. TableText({titles, dataRow}, "|_c") → dataTable