I. Functions, Graphs, and Limits

A.  Analysis of graphs.  With the aid of technology, graphs of functions are often easy to produce.  The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function.

C.  Asymptotic and unbounded behavior.

• Understanding asymptotes in terms of graphical behavior.
• Describing asymptotic behavior in terms of limits involving infinity.
• Comparing relative magnitudes of functions and their rates of change.  (For example, contrasting exponential growth, polynomial growth, and logarithmic growth.)

• An intuitive understanding of continuity.  (Close values of the domain lead to close values of the range.)
• Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem).