9.1.2 Piecewise Functions Key Objectives • Write, graph, and evaluate piecewise functions. • Use piecewise functions to describe real-world situations. Key Terms
• A piecewise function is a function that is a combination of one or more functions. • A step function is a piecewise function that is constant over each interval in its domain.
The rule for a piecewise function is different for different parts, or pieces, of the domain. Example 1 Retail Application
If the graph of a piecewise function contains three parts, then the rule for that function will be the combination of three function rules. The domain for the function will be divided into three intervals, where each piece of the function corresponds to one of the intervals. An open point on the function’s graph indicates that the corresponding x -value is not included in the domain. A closed endpoint on the function’s graph indicates that the corresponding x -value is included in the domain and is the endpoint for that interval of the domain. If a piece of a function has no endpoint, assume that the function continues to infinity. The piecewise function shown in the example below is composed of three horizontal line segments, which means that the value of the function remains constant for each interval of its domain. A piecewise function that is constant for each interval of its domain is called a step function.
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