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Hyperbolas (Rectangular) Explorations

Hyperbolas (Rectangular) Explorations
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2016-04-06 11:46
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and parameter variations of hyperbolas (rectangular). It involves core mathematical concepts including the definition of hyperbolas, asymptotes, linear regression, logarithmic functions, trapezoids, parallelograms, and polynomial functions. Construction highlights use GeoGebra commands and objects like f, g, h, p, q, r, s, t, f_1, g_1, h_1 to build hyperbolas and related shapes, with slider animations showing the effect of parameters on the shape. Suitable for high school and above mathematics education and exploration.

GeoGebra Commands & Parameters

  1. f(x) = 1 / x
  2. g(x) = 5 / x
  3. h(x) = 0.03 / x
  4. p(x) = 1 / (x + 5)
  5. q(x) = 3 / (x - 5)
  6. r(x) = 1 / x - 3
  7. s(x) = 7 / x + 1.4
  8. t(x) = (-(1 / x))
  9. f_1(x) = (-(0.2 / x))
  10. g_1(x) = (-(1 / (x + 5)))
  11. h_1(x) = (-(1 / x)) - 6