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

Phantom Graph of 1/(1-x^2)
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2018-07-15 10:03
FunctionCoordinate GeometryComplex Number
In collections Phantom Graphs
This example demonstrates the graph of the function 1/(1-x^2). Key mathematical concepts include function graphing, coordinate geometry, and complex numbers. Construction involves GeoGebra commands like ComplexRoot, Plane, CurveCartesian, and objects such as f, c, g, z_1, z_2, A_1, b, a, text1, A_2, text2. Suitable for high school students learning function properties and coordinate geometry applications.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw the graph of the function 1/(1-x^2), showing its relationship with complex numbers. First, create a plane, then plot the function graph, and finally connect the complex roots with dashed lines, labeling key points and the plane.
The prompt above was compiled from the original drawing commands and is for reference only.