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Logarithmic Transformations Demo

Logarithmic Transformations Demo
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2016-01-20 02:41
FunctionTransformationGraphing
This example demonstrates the transformations of logarithmic functions on the coordinate plane, including translations, scalings, and reflections. Key math concepts involve logarithmic functions, exponential functions, geometric transformations (translations, scalings, reflections), and the geometric meaning of function graphs. Construction highlights are derived from GeoGebra commands like objects b, h, k, a, c, n, f, A, B, C, d, g, D, E, m, used to define parameters and plot transformed function graphs. Suitable for high school mathematics teaching to help students visually understand the properties and transformation rules of logarithmic functions.

GeoGebra Commands & Parameters

  1. Numeric b(2.0)
  2. Numeric h(0.0)
  3. Numeric k(0.0)
  4. Numeric a(1.0)
  5. Numeric c(1.0)
  6. Numeric n(1.0)
  7. f(x) = (c * log(b, (a * (x - h)))) + k
  8. ((1 / a * (1 + h)), (c * (0 + k)))
  9. ((1 / a * (b + h)), (c * (1 + k)))
  10. ((1 / a * (1 / b + h)), (c * (-1 + k)))
  11. x = 0 + h
  12. g(x) = (c * log(1 / b, (a * (x - h)))) + k
  13. ((1 / a * (1 / b + h)), (c * (1 + k)))
  14. ((1 / a * (b + h)), (c * (-1 + k)))
  15. m(x) = (c * log((a * x) - h)) + k