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1C Zeros, Asymptotes and Points of Discontinuity

For the graph of a rational function, knowing whether a factor is in the numerator, denominator or both is key to understanding where zeros, asymptotes and points of discontinuity occur. Use the sliders to change the factors.
  1. Explain of a rule for each characteristic of the graph.
  2. Can a rational function have no asymptotes and no points of discontinuity?