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Function Transformation and Graphing

Function Transformation and Graphing
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2013-05-20 23:21
FunctionCoordinate Geometry
This example demonstrates how to graph the function f(x) = x^2 - 81 using GeoGebra and explore its transformation with the constant k=3, specifically f(k•x). Key math concepts include quadratic functions, function graph transformations, and scaling transformations. The construction involves commands/objects like Polygon, Line, Factor, Factors, Element, Intersect, If, Textfield, and Point. Suitable for high school students learning geometric transformations of function graphs.

GeoGebra Commands & Parameters

  1. Polygon((instructionEdge, y(Corner[1])), (instructionEdge, y(Corner[3])), Corner[4], Corner[1]) → instruction, e, g, h, i
  2. Line((x(Corner[1]) + ((2 * indent) * screenwidth), 0), yAxis) → align1
  3. Line((x(Corner[1]) + ((3 * indent) * screenwidth), 0), yAxis) → align2
  4. Line((x(Corner[1]) + ((4 * indent) * screenwidth), 0), yAxis) → align3
  5. Factor(f) → q
  6. Factors(f) → matrix1
  7. Factor(p) → r
  8. Factors(p) → matrix2
  9. Element(Element[matrix1, Length[matrix1] - 1], 1) → f1
  10. Element(Element[matrix1, Length[matrix1]], 1) → f2
  11. Element(Element[matrix2, Length[matrix2] - 1], 1) → p1
  12. Element(Element[matrix2, Length[matrix2]], 1) → p2
  13. Intersect(f, xAxis) → A, B
  14. Intersect(p, xAxis) → C, D
  15. If(abs(k) > 1, "narrower than", If[abs(k) < 1, "wider than", "the same width as"]) → width
  16. If(k > 1, "k >", If[k < 1, "0 < k <", "k ="]) → relation
  17. If(k > 1, "shrink horizontally", If[0 < k < 1, "expand horizontally", "appear unchanged"]) → motion
  18. Textfield(c) → inputBox1
  19. If(abs(k) > 1, "becomes smaller", If[abs(k) < 1, "becomes larger", "stays the same"]) → width2
  20. Intersect(f, yAxis, 1) → E
  21. Point(p) → F

AI Drawing Prompt Reference

Draw the graph of f(x) = x^2 - 81 and its transformation f(k•x) with k=3, marking the intersection points with the x-axis. Include text annotations describing the width changes and horizontal scaling of the transformed graph. Start by plotting the original function, then the scaled function, highlighting the y-axis intersection, and conclude with a text box for the function equation and notes on the graph's width and horizontal stretch/compression.
The prompt above was compiled from the original drawing commands and is for reference only.