Graphing Piecewise Functions: Using Constraints and Inequalities

This lesson teaches how to graph piecewise functions by leveraging knowledge of graphing other functions. It covers the use of open and closed circles in inequalities, defines piecewise functions, and explains how to graph each part of a piecewise function. The lesson also addresses common mistakes, such as not using constraints correctly, and concludes with a summary of the key points.

Explain the difference between open circles and closed circles in graphing inequalities.

What is the definition of a piecewise function?

How do you determine which expression to use in a piecewise function?

How do constraints affect the graph of a function?

Describe the process of graphing the first part of the function f(x) = -x + 1 when x is less than -1.

What does the solid dot at the end of the graph indicate when graphing f(x) = 2x for x greater than or equal to -1?

What is a common misunderstanding when graphing piecewise functions?