The limit is the fundamental notion of calculus. This underlying concept is the thread that binds together virtually all of the calculus studied by the student. In this lesson plan, the student's knowledge of limits will be extended using some common language and illustrated ideas through simple examples. The concept of limits will be used to describe functions with specific properties. Additionally, the concept of a limit function is further developed, and theorems for limits are analyzed and applied. Students will refer to these rules as they work through exercises.