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Square Root Transformations Demo

Square Root Transformations Demo
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2018-02-16 23:38
FunctionCalculusInequalityGraphing
This example demonstrates the graph of the square root function and its transformations. It involves core math concepts like function graphs, transformations, inequalities, and integrals. Construction highlights include using GeoGebra commands/objects such as n, k, h, a, b, f, square, Quadratic, h_1, cubic, j, absolute, k_1, l, p, text elements, and more. Suitable for high school mathematics students and teachers for function transformation instruction.

GeoGebra Commands & Parameters

  1. Numeric n(1)
  2. Numeric k(0)
  3. Numeric h(0)
  4. Numeric a(1)
  5. Numeric b(2.5)
  6. f(x) = (a * ((b * (x - h)))^(2)) + k
  7. Boolean square(true)
  8. Boolean Quadratic(false)
  9. h_1(x) = (a * (b * (x - h)^(3))) + k
  10. Boolean cubic(false)
  11. j(x) = (a * abs((b * (x - h)))) + k
  12. Boolean absolute(false)
  13. k_1(x) = x^(2)
  14. l(x) = x^(3)
  15. p(x) = abs(x)
  16. (h, k)
  17. g(x) = (a * sqrt((n * (x - h)))) + k

AI Drawing Prompt Reference

Draw a function transformation demo showing the square root function and its variations. The main curve is a square root graph passing through point (h, k), with parameters a, b, n controlling stretch and shift. Also display quadratic, cubic, and absolute value functions for comparison, all sharing the same vertex (h, k) and affected by the same parameters. Include adjustable sliders for numeric values and toggles to show or hide each function type. Use a coordinate grid with axes, color-coded curves, and labeled key points. The scene illustrates translations and scaling of functions.
The prompt above was compiled from the original drawing commands and is for reference only.