Understanding functions

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After completing this section, students should be able to do the following.

State the definition of a function.
Find the domain and range of a function.
Distinguish between functions by considering their domains.
Determine where a function is positive or negative.
Plot basic functions.
Perform basic operations and compositions on functions.
Work with piecewise defined functions.
Determine if a function is one-to-one.
Recognize different representations of the same function.
Define and work with inverse functions.
Plot inverses of basic functions.
Find inverse functions (algebraically and graphically).
Find the largest interval containing a given point where the function is invertible.
Determine the intervals on which a function has an inverse.