Wednesday 14 April 2021

Rational Functions and Asymptotes

Consider the rational function given by two polynomial functions;


What about these two polynomials decides the location of:

  • The vertical asymptotes?
  • The horizontal asymptotes?
  • The solutions to f(x)=0?
I know the theory behind this, but what does it look like in motion?

The geogebra file linked here https://www.geogebra.org/m/m8eqsjzu explores this. What happens as I click and drag one of the curves? How does it make the graph of f(x) move?

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