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Inverse Function Graphing and Verification

Inverse Function Graphing and Verification
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2016-07-07 19:55
FunctionCoordinate GeometryCalculusGraphing
In collections Fun with Functions
This example demonstrates how to graph an inverse function by reflecting the original function about the line y=x and tests if the new curve is a function. It illustrates the One-to-One requirement for inverse functions. The construction uses GeoGebra commands like Sequence, Mirror, Zip, Max, Textfield, Point, Vector, Tangent, and ParametricDerivative. Suitable for high school mathematics education to help students understand the properties and determination criteria of inverse functions.

GeoGebra Commands & Parameters

  1. Sequence(x = j, j, c1, c3, (c3 - c1) / 20) → vlines
  2. Mirror(f, g) → f_{inverse}
  3. Zip({Intersect[vl, f_{inverse}]}, vl, vlines) → isects
  4. Zip(Length[in], in, isects) → list2
  5. Max(list2) → a
  6. Textfield(f) → InputBox1
  7. Point(xAxis) → A
  8. Vector(A, B) → u
  9. Vector(B, C) → v
  10. Vector(C, D) → w
  11. Vector(D, E) → b
  12. Vector(E, F) → c
  13. Vector(F, A) → d
  14. Tangent(B, f) → h
  15. ParametricDerivative(f_{inverse}) → pder