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The Exponential Function as an Isomorphism

The Exponential Function as an Isomorphism
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2019-10-04 01:54
VectorFunctionGeometric ConstructionGraphing
This example demonstrates how exponential functions and their inverses preserve structural properties, showcasing the concept of isomorphism. Key math concepts include exponential functions, logarithms, function inverses, and vector operations. GeoGebra commands like Point, CircleArc, Tangent, Rotate, Textfield, Vector, Midpoint, Mirror, and Segment are used to construct the visual representation. Suitable for high school and advanced learners exploring function properties and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Point(yAxis) → A
  3. CircleArc(C, B, A) → c
  4. Tangent(B, c) → d,
  5. Point(d) → E
  6. Rotate(E, 8°, B) → E'
  7. Textfield(b) → inputBox1
  8. Vector(F, B) → u
  9. Midpoint(A, B) → G
  10. Mirror(c, G) → c'
  11. Mirror(F, G) → F'
  12. Vector(F', A) → w
  13. Point(yAxis) → H
  14. Point(a) → I
  15. CircleArc(J, I, H) → k
  16. CircleArc(K, H, I) → p
  17. Vector(L, I) → i
  18. Vector(M, H) → j
  19. Segment(U, T) → m
  20. Segment(W, V) → n
  21. Midpoint(m) → R
  22. Midpoint(n) → S
  23. CircleArc(Z, O, N) → s
  24. CircleArc(A_1, N, O) → c_1
  25. Vector(R, N) → u_1
  26. Vector(S, O) → r
  27. Midpoint(A, T) → B_1
  28. Midpoint(B, V) → C_1
  29. Midpoint(I, W) → D_1
  30. Midpoint(H, U) → E_1
  31. Segment(B_1, T) → q
  32. Segment(C_1, V) → f_1
  33. Segment(D_1, W) → g_1
  34. Segment(E_1, U) → h_1
  35. Midpoint(H, K) → F_1
  36. Midpoint(Z, O) → G_1