Section 1
Definition and Notation of Piecewise Functions
Property
A piecewise function is defined by different equations over different intervals of its domain. The general notation is:
In this Grade 9 lesson from California Reveal Math Algebra 1, students learn to identify and graph piecewise-defined functions, piecewise-linear functions, step functions, and the greatest integer function. Students practice graphing multi-rule functions by plotting each piece over its specified domain interval, using open and closed endpoints to indicate strict versus inclusive inequalities. Real-world contexts like swim team age groups help illustrate how step functions model situations where output values change abruptly at defined boundaries.
Section 1
Definition and Notation of Piecewise Functions
A piecewise function is defined by different equations over different intervals of its domain. The general notation is:
Section 2
Graphing Piecewise Functions with Boundary Points
When graphing piecewise functions, use closed circles (•) to indicate points included in the domain of a piece, and open circles (○) to indicate points not included. At boundary points where domain intervals meet, only one piece can contain the boundary value.
Section 3
Evaluating Piecewise Functions at Specific x-Values
To evaluate a piecewise function at , identify which interval condition satisfies, then substitute into only that piece's expression.
For a piecewise function such as:
Section 4
Graphing Piecewise Functions
To graph a piecewise function, we plot each piece separately on its specified domain, then combine them into one graph. Each piece is graphed only over its defined interval, and we use open or closed circles to indicate whether endpoints are included.
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Section 1
Definition and Notation of Piecewise Functions
A piecewise function is defined by different equations over different intervals of its domain. The general notation is:
Section 2
Graphing Piecewise Functions with Boundary Points
When graphing piecewise functions, use closed circles (•) to indicate points included in the domain of a piece, and open circles (○) to indicate points not included. At boundary points where domain intervals meet, only one piece can contain the boundary value.
Section 3
Evaluating Piecewise Functions at Specific x-Values
To evaluate a piecewise function at , identify which interval condition satisfies, then substitute into only that piece's expression.
For a piecewise function such as:
Section 4
Graphing Piecewise Functions
To graph a piecewise function, we plot each piece separately on its specified domain, then combine them into one graph. Each piece is graphed only over its defined interval, and we use open or closed circles to indicate whether endpoints are included.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter