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Function Transformations with Horizontal Stretch

Function Transformations with Horizontal Stretch
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2020-09-05 03:40
FunctionTransformationGraphing
This example illustrates how to apply a horizontal stretch transformation to a function graph. It covers key concepts such as scaling factors, coordinate mapping, and the effect of horizontal dilation on the shape of the graph. The GeoGebra construction uses Random, RandomElement, RandomDiscrete, If, and Textfield commands to create interactive input boxes and buttons, allowing users to adjust parameters and see the updated function f_{new} instantly. It is designed for high‑school or early university students learning function transformations and can serve as an interactive classroom demonstration or a self‑paced exploration activity.

GeoGebra Commands & Parameters

  1. Random(-4, 4) → r
  2. RandomElement({-2, -3 / 2, -1, -1 / 2, 1 / 2, 1, 3 / 2, 2}) → m
  3. RandomElement({-3, -2, -1, 1, 2, 3}) → n
  4. Random(-5, 5) → p
  5. RandomElement({-2, -1, 1, 2}) → q
  6. RandomDiscrete({1, 2, 3, 4, 5}, {1, 1, 3, 3, 10}) → whatweget
  7. RandomElement({-3, -2, -1, -1 / 2, -1 / 3, 1 / 3, 1 / 2, 1, 2, 3}) → b
  8. If(whatweget ≟ 1, A, whatweget ≟ 2, B, whatweget ≟ 3, C, whatweget ≟ 4, D, whatweget ≟ 5, E) → f
  9. RandomElement({-3, -2, -1, -1 / 2, 1 / 2, 1, 2, 3}) → a
  10. Random(-6, 6) → c
  11. Random(-6, 6) → d
  12. RandomDiscrete({1, 2, 3, 4}, {67, 67, 33, 33}) → ShowProblem
  13. Textfield(a1) → InputBox1
  14. Textfield(c1) → InputBox2
  15. Textfield(d1) → InputBox3
  16. Textfield(m_{1}) → InputBox4
  17. Textfield(x_{1}) → InputBox5
  18. Textfield(y_{1}) → InputBox6
  19. Textfield(a_{L1}) → InputBox7
  20. Textfield(b_{L1}) → InputBox8
  21. Textfield(m_{2}) → InputBox9
  22. Textfield(x_{2}) → InputBox10
  23. Textfield(y_{2}) → InputBox11
  24. Textfield(a_{L2}) → InputBox12
  25. Textfield(b_{L2}) → InputBox13
  26. Textfield(m_{3}) → InputBox14
  27. Textfield(x_{3}) → InputBox15
  28. Textfield(y_{3}) → InputBox16
  29. Textfield(a_{L3}) → InputBox17
  30. Textfield(b_{L3}) → InputBox18
  31. Textfield(w) → InputBox19
  32. Textfield(a_{h}) → InputBox20
  33. Textfield(b_{h}) → InputBox21
  34. Textfield(a_{C}) → InputBox22
  35. Textfield(b_{C}) → InputBox23
  36. Textfield(y_{C}) → InputBox24
  37. Textfield(y_{P}) → InputBox25
  38. Textfield(b1) → InputBox26

AI Drawing Prompt Reference

Please draw a graphic illustrating a horizontal stretch transformation of a function. Include an original function graph, such as y=x^2, and a transformed function graph whose shape is obtained by stretching the original graph horizontally. Add input boxes to enter the stretch factor and display the transformed function. The construction order: first draw the original function graph, then draw the transformed function graph based on the value entered in the input box, and finally add the input boxes to allow users to adjust parameters and view the result in real time.
The prompt above was compiled from the original drawing commands and is for reference only.