When analyzing a function, we would like to know the function’s domain and range; the function’s zeros; intervals where the function is increasing and decreasing; global maximum and minimum values of the function; local maximum and minimum values of the function; discontinuities and singularities and behavior around them; intervals of continuity; end-behavior; and what the graph looks like.

$\blacktriangleright$ We would like to describe this information exactly, but will settle for approximation when exactness is not possible. Even when we approximate, we would like exact information about our approximations.

As we develop our library of elementary functions, we will collect information on these characteristics and features of each function family. Currently, our library contains linear and quadratic functions.

A parallel story line is that of piecewise defined functions. Gluing pieces of functions together is one of our first methods to create functions beyond our library of elementary functions.

In this section, we will begin to analyze piecewise functions created from pieces and parts of linear and quadratic functions.

Learning Outcomes

In this section, students will

• identify discontinuites.
• identify maximum and minimum values.
• identify function zeros.
• state intervals where function is increasing and decreasing.
• state domains and ranges.