Vertical Stretches, Compressions, and Reflections

Vertical Stretches, Compressions, and Reflections
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2015-10-29 22:17
This example demonstrates the transformations of function graphs including vertical stretches, compressions, and reflections. Key math concepts involved are function transformations, vertical scaling (stretching or compressing), and reflection (across the x-axis or y-axis). It is constructed using GeoGebra commands like Curve(Cartesian), Point, and Vector, along with objects such as sliders to control transformation parameters. Suitable for high school students learning about function transformations and analytical geometry, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, t^(2), t, -2.8, 2.8) → f1
  2. Point(f1) → A
  3. Vector(A, B) → u
  4. Point(f1) → C
  5. Vector(C, D) → v
  6. CurveCartesian(t, t^(3), t, -1.8, 2.01) → f2
  7. Point(f2) → E
  8. Vector(E, F) → w
  9. Point(f2) → G
  10. Vector(G, H) → g
  11. CurveCartesian(t, abs(t), t, -5, 5) → f3
  12. Point(f3) → I
  13. Vector(I, J) → h
  14. Point(f3) → K
  15. Vector(K, L) → i
  16. CurveCartesian(t, sqrt(t), t, 0, 9.2) → f4
  17. Point(f4) → M
  18. Vector(M, N) → j
  19. CurveCartesian(t, cbrt(t), t, -8.1, 8.1) → f5
  20. Point(f5) → O
  21. Vector(O, P) → k
  22. Point(f5) → Q
  23. Vector(Q, R) → l