Algebra 2. Graphing Piecewise functions

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What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

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How do you graph a piecewise function?

Back

To graph a piecewise function, identify the intervals for each piece, graph each piece according to its formula, and ensure to use open or closed dots to indicate whether endpoints are included.

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What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces meet.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, which may vary for different pieces.

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What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce.

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How do you determine the endpoints of a piecewise function?

Back

Endpoints are determined by the intervals defined in the piecewise function. Check the inequalities to see if they are included (closed dot) or excluded (open dot).

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What is the significance of open and closed intervals in piecewise functions?

Back

Open intervals indicate that the endpoint is not included in the function (open dot), while closed intervals indicate that the endpoint is included (closed dot).

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Can a piecewise function be linear?

Back

Yes, a piecewise function can consist of linear segments, each defined over specific intervals.

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What is a common mistake when graphing piecewise functions?

Back

A common mistake is not using the correct type of dot (open or closed) at the endpoints of the intervals.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding formula.