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.

Tags

CCSS.HSF-IF.C.7B

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

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To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression for that interval.

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CCSS.HSF.IF.A.2

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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, which may vary across different pieces.

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What does the notation f(x) mean in the context of piecewise functions?

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In piecewise functions, f(x) represents the output value of the function for a given input x, determined by the specific piece of the function that applies to that x.

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How can you graph a piecewise function?

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To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Tags

CCSS.HSF-IF.C.7B

Front

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

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Endpoints in a piecewise function indicate the boundaries of the intervals; whether they are included or excluded affects the function's continuity.

Tags

CCSS.HSF-IF.C.7B

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

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To find the value of a piecewise function at a boundary point, check both pieces of the function to see if the boundary point is included in either piece.

Tags

CCSS.HSF.IF.A.2

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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 output values (y-values) that the function can produce, which may vary across different pieces.

Tags

CCSS.HSF-IF.C.7B

Front

What is the difference between a continuous and a discontinuous piecewise function?

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A continuous piecewise function has no breaks or jumps in its graph, while a discontinuous piecewise function has breaks or jumps at certain points.

Tags

CCSS.HSF-IF.C.7B

Front

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

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To determine if a piecewise function is increasing or decreasing, analyze the slopes of the pieces over their respective intervals.