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Phantom Graph 2x^2/(x^2-1) Function Plotting

Phantom Graph 2x^2/(x^2-1) Function Plotting
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2018-07-15 10:11
FunctionCoordinate GeometryComplex NumberGraphing
In collections Phantom Graphs
This example demonstrates the plotting of the function y=2x^2/(x^2-1), highlighting its asymptotes and symmetry. Core mathematical concepts include function graphs, horizontal and vertical asymptotes, symmetry about the y-axis, rational functions, and analytical geometry. It utilizes GeoGebra commands like ComplexRoot, Plane, and CurveCartesian. Suitable for high school students to understand the characteristics of rational function graphs and the application of complex number concepts.

GeoGebra Commands & Parameters

  1. ComplexRoot((2 * x^(2)) - (c * (x^(2) - 1))) → z_1, z_2
  2. Plane((0, c, 0), (1, c, 1), (-1, c, 3)) → b
  3. CurveCartesian(0, (2 * t^(2) / (t^(2) + 1)), t, t, -25, 25) → a