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Transformations of Sine Function f(x)=a sin(bx)+d

Transformations of Sine Function f(x)=a sin(bx)+d
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2019-06-06 23:39
FunctionTrigonometrySlider AnimationGraphing
In collections Sine and Cosine Functions
This GeoGebra example dynamically demonstrates the transformation of the sine function in the form f(x) = a sin(bx) + d, using sliders to adjust parameters a (amplitude), b (frequency/period), and d (vertical shift). It visually illustrates how each parameter affects the graph's shape, including stretching/compressing, horizontal shifting, and vertical translation. The construction utilizes function objects, sliders, and text annotations to support interactive learning. Ideal for high school trigonometry, function transformation units, or introductory calculus wave analysis. It reinforces the relationship between algebraic parameters and graphical properties, enabling students to explore and conjecture independently.

GeoGebra Commands & Parameters

  1. f1(x) = (4 * cos(x°))
  2. f2(x) = (-3 * cos(x°))
  3. f3(x) = (2 * sin(x°)) + 4
  4. f4(x) = (-2 * sin(x°)) + 4
  5. f5(x) = (3 * cos(x°)) - 2
  6. f6(x) = (-4 * sin(x°)) + 1
  7. f7(x) = cos(((2 * x))°) + 1
  8. f8(x) = sin(((2 * x))°) - 3
  9. f9(x) = (3 * cos(((4 * x))°))
  10. f10(x) = (5 * sin(((6 * x))°))
  11. f11(x) = (4 * sin(((3 * x))°)) + 1
  12. f12(x) = (-2 * sin(((4 * x))°)) - 3
  13. Numeric q(1.0)
  14. Numeric a(12.0)
  15. Boolean b(false)

AI Drawing Prompt Reference

Draw multiple sine function graphs, adjust amplitude, frequency, and vertical shift using sliders to demonstrate the transformation process, including stretching/compressing, horizontal shifting, and vertical translation, with text annotations explaining the effect of each parameter on the graph.
The prompt above was compiled from the original drawing commands and is for reference only.