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Inverse Functions Algebra Practice: Interactive Function Inversion

Inverse Functions Algebra Practice: Interactive Function Inversion
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2020-11-26 15:58
FunctionTransformationSlider AnimationGraphing
In collections Grade 12 PreCalculus BC
① This example demonstrates how to find the inverse of given functions algebraically and dynamically displays the relationship between the original function and its inverse in GeoGebra. ② Core mathematical concepts include the definition of inverse functions, swapping domain and range, the identity property f(f⁻¹(x))=x, and simplification of rational functions. ③ Construction highlights: using GeoGebra commands such as GCD, Simplify, Shuffle, If, Invert, FractionText, Point, and Corner, the applet builds multiple function objects (f1, f2, f4, f5) and their inverses (f1inv, f4inv, f5inv), with buttons (button1, button2) to generate random questions and check answers, and lists (alist, blist, qlist) to manage answer choices. ④ Suitable for high school or pre-university students learning functions and inverse functions, this interactive tool supports classroom practice or self-study, reinforcing algebraic inversion techniques and the symmetry of graphs.

GeoGebra Commands & Parameters

  1. GCD({f4c, (f4c * f4b) + f4a}) → f4gcd
  2. Simplify((((x * f4gcd) * f4b) + f4a - (f4c * f4b)) / ((f4gcd * x) - f4c)) → f4inv
  3. GCD(fa, fb) → f1gcd
  4. Shuffle(qlist) → qsh, {1, 2, 4, 3, 5}
  5. GCD({fa, fb}) → f5gcd
  6. Simplify(((fa * x) + fb) / f1gcd) → f1
  7. Simplify(x^(2) + (fa * x) + fb) → f2
  8. Simplify((f4a / (x - f4b) + f4c) / f4gcd) → f4
  9. If(question ≟ 1, Element[qsh, 1], If[question ≟ 2, Element[qsh, 2], If[question ≟ 3, Element[qsh, 3], If[question ≟ 4, Element[qsh, 4], Element[qsh, 5]]]]) → qQ
  10. Invert(f1) → f1inv
  11. Invert(f5) → f5inv
  12. If(qQ ≟ 1, f1, If[qQ ≟ 2, f2, If[qQ ≟ 3, f2, If[qQ ≟ 4, f4, If[qQ ≟ 5, f5]]]]) → f
  13. FractionText(f4dom) → f3domtxt
  14. FractionText(f5int) → f5inttext
  15. If(qQ ≟ 1, ftext1, If[qQ ≟ 2, ftext2, If[qQ ≟ 3, ftext3, If[qQ ≟ 4, ftext4, ftext5]]]) → ftext
  16. If(qQ ≟ 1, f1invtxt, If[qQ ≟ 2, f2invtxt, If[qQ ≟ 3, f3invtxt, If[qQ ≟ 4, f4invtxt, f5invtxt]]]) → finvtxt
  17. Point(yAxis) → SC1A
  18. Point(sc12) → SC1D
  19. Point(sc12) → SC1E
  20. Point(sc12) → SC1F
  21. Corner(5) → dims

AI Drawing Prompt Reference

Create an interactive graph showing the dynamic relationship between original functions and their inverses for algebra practice. Include multiple function objects and their inverses, with buttons to generate random questions and check answers. Use lists to manage options, points to mark key positions, and display function expressions and domains. Highlight the symmetry of original and inverse function graphs about the line y=x, suitable for high school students learning function inversion and graph symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.