The study of a function

  1. Domain

  2. Symmetries

  3. Intersection with the axes

  4. Sign of the function

  5. Point of discontinuity (vertical asymptotes)

  6. If the domain is unbounded investigate the behavior of the function looking for horizontal or oblique asymptotes

  7. f'(x): maxima, minima and critical points, monotonicity

  8. f''(x): concavity/convexity, inflextion points