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Horizontal Stretch Root Function

Horizontal Stretch Root Function
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2015-04-30 21:27
FunctionOptimization
This example demonstrates the horizontal stretch transformation of root functions (e.g., square root function). Key math concepts include function transformations, horizontal stretch coefficients, and the characteristics of root function graphs. Construction highlights involve GeoGebra objects/commands: f (function), A/B/C/D (points), b (slider), g (function graph), F/E/G/H (points), a/c/d (points). Suitable for high school students to learn and explore the properties of function transformations, ideal for classroom instruction or self-study.

GeoGebra Commands & Parameters

  1. f(x) = sqrt(x)
  2. (0, f(0))
  3. (1, f(1))
  4. (4, f(4))
  5. (9, f(9))
  6. Numeric b(1.0)
  7. g(x) = sqrt((b * x))
  8. (1 / b, g(1 / b))
  9. (0 / b, g(0 / b))
  10. (4 / b, g(4 / b))
  11. (9 / b, g(9 / b))
  12. Line a(0.0, 1.0, -1.0)
  13. Line c(0.0, 1.0, -2.0)
  14. Line d(0.0, 1.0, -3.0)

AI Drawing Prompt Reference

Draw a horizontal stretch of the root function. Start by plotting the function y=√x, then create a slider b to adjust the horizontal stretch. Next, plot the new function y=√(b*x) and mark the points where x=1, 4, 9. Finally, draw three horizontal lines representing y=1, y=1/2, y=1/3.
The prompt above was compiled from the original drawing commands and is for reference only.