Unit 1: Functions, Graphs, and Limits
This unit begins with a review of functions that should have been learned in a previous course. Specifically, we will examine the relationship between formulas and graphs of functions, as well as general properties of their graphs. After completing the first part of this unit, you should feel comfortable explaining general patterns that occur in certain types of functions, as well as be able to give specific information about a graph given its formula. After studying functions, we will examine the first "big" topic in calculus, the limit. As you will see, much of calculus is based on this concept, so it is important to have a good understanding of its fundamental meaning now. We will study limits as they relate to graphs and formulas, and we will use formal limit notation to explain certain behaviors of graphs that you have studied before (such as continuity), but without the concept of limits. This is a very exciting unit and it is important to understand limits well before moving on to the next part of the course.
Completing this unit should take you approximately 15 hours.