Basic Properties of Real Functions: Survey of Methods

If you wish to simultaneously follow another text on properties of functions in a separate window, click here for Theory and here for Solved Problems.

Here we offer manuals for the following topics:

• Domain.
• Boundedness.
• Symmetry.
• Periodicity.
• Continuity.
• 1-1 and inverse.
• Transformations and graph guessing.

We do not offer a section on monotonicity, since this is rarely done by the definition. If you are curious how it can be done, check on the corresponding problems in Solved Problems - Basic properties, especially this one.

Monotonicity and concavity are usually done using derivatives, the appropriate methods are explained in Derivatives - Method Survey - Graphing functions.