Piecewise Functions

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What is a piecewise function?

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

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CCSS.HSF-IF.C.7B

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How do you evaluate a piecewise function?

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To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

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CCSS.HSF.IF.A.2

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What does the graph of a piecewise function look like?

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The graph of a piecewise function consists of multiple segments, each representing a different expression for specific intervals.

Tags

CCSS.HSF-IF.C.7B

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What is the domain of a piecewise function?

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The domain of a piecewise function is the set of all input values (x-values) for which the function is defined.

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What is the range of a piecewise function?

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

Tags

CCSS.HSF-IF.C.7B

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What does it mean for a function to be continuous?

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A function is continuous if there are no breaks, jumps, or holes in its graph.

Tags

CCSS.HSF-IF.C.7B

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What is a discontinuity in a piecewise function?

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A discontinuity occurs when there is a break in the graph of the function, often at the points where the pieces meet.

Tags

CCSS.HSF-IF.C.7B

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How can you determine if a piecewise function is increasing or decreasing?

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You can determine if a piecewise function is increasing or decreasing by analyzing the slopes of the segments in its graph.

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What is the significance of the endpoints in a piecewise function?

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Endpoints indicate where one piece of the function ends and another begins, and they can be included or excluded from the domain.

Tags

CCSS.HSF-IF.C.7B

Front

How do you find the value of a piecewise function at a specific point?

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To find the value at a specific point, substitute the point into the appropriate piece of the function based on its interval.

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CCSS.HSF.IF.A.2