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Phantom Graph for f(x)=x^4

Phantom Graph for f(x)=x^4
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2018-07-15 09:05
FunctionComplex NumberGraphing
In collections Phantom Graphs
This example demonstrates the phantom graph for the function f(x)=x^4. It involves the concept of function graphing. Using commands like Plane, ComplexRoot, and CurveCartesian, the graph of f(x)=x^4 can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw the graph of the function f(x)=x^4, including its four complex roots and the graph on the real plane. First, draw a plane, then find the four complex roots of the function at c, and finally, draw the graph of the function for positive and negative real numbers.
The prompt above was compiled from the original drawing commands and is for reference only.