Look for periodicity.

  Analyze continuity.

  Analyze differentiability : existence of .

  Locate intervals of increase, decrease.

  Find critical points.

  Analyse behaviour of at critical points to locate points of local extrema.

  Locate regions of convexity, concavity.

  Locate points of inflection.

  Analyse.

  Locate horizontal asymptotes:.

  Locate vertical asymptotes:.

  Locate oblique asymptotes.