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Phantom Graph x^4/(1-x^2) Function Plotting

Phantom Graph x^4/(1-x^2) Function Plotting
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2018-07-16 03:30
FunctionCalculusDerivativeComplex NumberGraphing
In collections Phantom Graphs
This example demonstrates how to plot and analyze the function f(x)=x^4/(1-x^2) and its properties. Key math concepts include function graphs, odd/even symmetry, asymptotes, extrema, and complex roots. Construction highlights from the summary involve commands like ComplexRoot, Plane, and CurveCartesian in GeoGebra. Suitable for high school and above learners for understanding complex function plotting and analysis.

GeoGebra Commands & Parameters

  1. ComplexRoot(x^(4) - (c * (1 - x^(2)))) → z_1, z_2, z_3, z_4
  2. Plane((0, c, 0), (1, c, 1), (-1, c, 3)) → a
  3. CurveCartesian(t, (-4 * t^(2)) + (2 * sqrt((4 * t^(2)) + 1)) - 2, sqrt((-t^(2)) - 1 + sqrt((4 * t^(2)) + 1)), t, (-sqrt(2)), sqrt(2)) → d
  4. CurveCartesian(t, (-4 * t^(2)) + (2 * sqrt((4 * t^(2)) + 1)) - 2, (-sqrt((-t^(2)) - 1 + sqrt((4 * t^(2)) + 1))), t, (-sqrt(2)), sqrt(2)) → e
  5. CurveCartesian(0, t^(4) / (1 + t^(2)), t, t, -25, 25) → g