The goal of Precalculus is to become familiar with the Elementary Functions, functions we build with these, and HOW to analyze them. You already know some of these functions.

These are our basic building blocks for functions. We will examine their formulas and graphs. We will identify important features of each type. We will measure their rates of change.

From these building blocks we build some very sophisticated and complex functions through the usual arithmetic operations and a new operation called composition.

Separate from those types of combinations, we also create new functions by cutting the Elementary Functions into pieces and gluing them together into odd shapes. These are called piecewise defined functions. Piecewise defined functions are especially handy for illustrating the rich and weird structure of functions.

We have several well-known functions that are piecewise defined functions. Among these are the absolute value function and the greatest integer function.

We will explore these as well as more general piecewise defined functions in this section.

Learning Outcomes

In this section, students will

• evaluate piecewise functions.
• graph piecewise functions.
• solve equations involving piecewise functions.
• solve inequalities involving piecewise functions.