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Reflection and axial symmetry

This model illustrates a process of construction a graph of 1/(2x2-1)2 from a graph of function f(x) = x2.

  • x2 stretches to 2x2 and shifts down to 2x2 - 1, the function is even as x2;
  • the function is raised to the power of 2, zeroes of the function remain the same, the function is even and positive;
  • Construct the resulted graph of 1/(2x2-1)2. The zeroes of function transform to infinity (vertical asymptotes), if x tends to infinity then function tends to zero. The transformation is completed.

The model is a movie. To navigate through the movie use Play, Pause, Stop, Previous step and Next step buttons.

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