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Phantom Graph of y=x^2/(x-1)

Phantom Graph of y=x^2/(x-1)
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2018-07-15 11:00
FunctionCoordinate GeometryCalculus
In collections Phantom Graphs
This example demonstrates the graph of the function y=x^2/(x-1) and its unusual behavior, particularly the discontinuity at x=1. Key mathematical concepts include discontinuities, asymptotes, and function graphing. It uses GeoGebra commands/objects like ComplexRoot, Plane, CurveCartesian for construction. Suitable for high school and above students to learn function properties and graphing techniques.

GeoGebra Commands & Parameters

  1. ComplexRoot(x^(2) - (c * (x - 1))) → z_1, z_2
  2. Plane((0, c, 0), (1, c, 1), (1, c, -2)) → a
  3. CurveCartesian(t, (2 * t), sqrt((2 * t) - t^(2)), t, 0, 2) → b
  4. CurveCartesian(t, (2 * t), (-sqrt((2 * t) - t^(2))), t, 0, 2) → d