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Function Transformations by Vincent Shuali

Function Transformations by Vincent Shuali
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2018-09-21 01:31
FunctionTrigonometryTransformationGraphing
This example demonstrates the concept of function transformations, including translations and scalings. It involves core mathematical concepts such as functions, linear functions, polynomial functions, power functions, quadratic functions, trigonometric functions, and step functions. Using GeoGebra commands like Sequence, Element, Textfield, If, and Vector, it dynamically shows changes in function graphs. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(x_{min} + (i * (x_{max} - x_{min}) / (N - 1)), i, 0, N - 1) → X
  2. Element(X, H2) → I2
  3. Textfield(f) → InputBox1
  4. If(a_x ≟ 1, If[a_y ≠ 1, (a_y * f(x - x_0)) + y_0, f(x - x_0) + y_0], If[a_y ≠ 1, (a_y * f((x - x_0) / a_x)) + y_0, f((x - x_0) / a_x) + y_0]) → g
  5. Vector(F2, E2) → G2_1
  6. Vector(F3, E3) → G3
  7. Vector(F4, E4) → G4
  8. Vector(F5, E5) → G5
  9. Vector(F6, E6) → G6
  10. Vector(F7, E7) → G7
  11. Vector(F8, E8) → G8
  12. Vector(F9, E9) → G9
  13. Vector(F10, E10) → G10
  14. Vector(F11, E11) → G11
  15. Vector(F12, E12) → G12
  16. Vector(F13, E13) → G13
  17. Vector(F14, E14) → G14
  18. Vector(F15, E15) → G15
  19. Vector(F16, E16) → G16
  20. Vector(F17, E17) → G17
  21. Vector(F18, E18) → G18
  22. Vector(F19, E19) → G19
  23. Vector(F20, E20) → G20
  24. Vector(F21, E21) → G21
  25. Element(X, H3) → I3
  26. Element(X, H4) → I4
  27. Element(X, H5) → I5
  28. Element(X, H6) → I6
  29. Element(X, H7) → I7
  30. Element(X, H8) → I8
  31. Element(X, H9) → I9
  32. Element(X, H10) → I10
  33. Element(X, H11) → I11
  34. Element(X, H12) → I12
  35. Element(X, H13) → I13
  36. Element(X, H14) → I14
  37. Element(X, H15) → I15
  38. Element(X, H16) → I16
  39. Element(X, H17) → I17
  40. Element(X, H18) → I18
  41. Element(X, H19) → I19
  42. Element(X, H20) → I20
  43. Element(X, H21) → I21

AI Drawing Prompt Reference

Create a dynamic graph illustrating function transformations, focusing on translations and scalings. The graph should feature an original function curve, such as a trigonometric or quadratic function, and a transformed curve derived via horizontal and vertical shifts, along with horizontal and vertical scalings. Use a sequence of points to define the domain and represent transformation parameters with vectors. The graph must interactively show real-time changes as parameters are adjusted, suitable for high school math education.
The prompt above was compiled from the original drawing commands and is for reference only.