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Mirroring Functions

Mirroring Functions
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2023-03-13 04:36
FunctionCalculusGeometric ConstructionSlider AnimationGraphing
In collections geometriadinamica.es
This example demonstrates how to observe function images in a mirror, constructing mirrored points, segments, and orthogonal lines to showcase the symmetry of functions. Core mathematical concepts include exponential functions, median, Riemann sums, frequency distribution, and subtraction. Construction highlights involve using GeoGebra commands such as Point, Intersect, Segment, OrthogonalLine, Line, Mirror, Angle, Distance, and Ellipse. Suitable for high school and above mathematics learners and educators to understand function transformations and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(yAxis) → F
  2. Intersect(xAxis, yAxis) → B_2
  3. Segment(B_2, F) → b
  4. Intersect(b, g) → A
  5. OrthogonalLine(L, b) → i
  6. Intersect(b, i) → B
  7. OrthogonalLine(C, b) → e
  8. Point(e) → I
  9. Point(e) → J
  10. Segment(J, I) → h
  11. Point(h) → H
  12. Intersect(c, i) → M
  13. Line(B_1, B_2) → d
  14. OrthogonalLine(B_1, d) → f
  15. Mirror(pic1, b) → pic2
  16. Mirror(H, b) → D
  17. OrthogonalLine(E, b) → a
  18. Intersect(a, c) → G
  19. Intersect(g, c) → K
  20. Mirror(M, b) → N
  21. Mirror(K, b) → O
  22. Segment(G, O) → j
  23. Segment(G, N) → k
  24. Intersect(b, j) → A'
  25. Intersect(b, k) → B'
  26. Angle(B', G, A') → α
  27. Segment(A', B') → l
  28. Mirror(O, b) → P
  29. Mirror(N, b) → Q
  30. Segment(P, A') → m
  31. Segment(B', Q) → n
  32. Distance(N, M2) → o
  33. Ellipse(N2, O2, o) → p
  34. Segment(G, O2) → q
  35. Segment(G, N2) → r
  36. Distance(M3, B') → s
  37. Intersect(q, l) → R
  38. Intersect(r, l) → S
  39. Ellipse(R, S, s) → t

AI Drawing Prompt Reference

Draw a function graph and its mirror image. Start by taking point F on the y-axis and point B2 at the intersection of the x-axis and y-axis, then draw line segment b connecting B2 and F. Next, take point A on the function graph g, construct a line i perpendicular to b, and find intersection point B. Continue by constructing a line e perpendicular to C, taking points I and J, drawing line segment h, and selecting point H on h. Through mirroring, construct pic2, D, a, f, and the mirror image of pic1, ultimately forming several line segments and ellipses to demonstrate the function graph and its mirror image.
The prompt above was compiled from the original drawing commands and is for reference only.