Functions - Exercises

Here you will find problems for practicing. Each problem has hints coming with it that can help you if you get stuck.
Remark concerning limits: If you want to practice the mechanics of various methods (limit algebra, l'Hospital's rule, cancelling, etc.), go to Basic methods. If you think that you mastered those methods and need practice in recognizing which method to use in a particular limit, go to Common limits. Tougher standard limits use common methods, but the calculations are more demanding.

• Domain of a function
• Basic properties: symmetry, periodicity, continuity
• 1-1 and inverse function
• Limits of functions:
  • Basic methods
  • Common limits
  • Tougher standard limits
  • Limits with parameter and Interesting limits
• Domain and limits at endpoints of intervals
• Graph sketching using transformations

Exercises on related topics are also in Derivatives - Exercises in the sections Graphing functions - Individual steps and in Graphing functions. In particular we use information on domain and limits there, determine asymptotes and we also investigate monotonicity and concavity using derivative (the standard procedure).
Implicit and parametric functions have their own section in Derivative - Exercises.