Piece-Wise Functions Practice

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What is a piece-wise function?

Back

A piece-wise function is a function that is defined by different expressions or formulas for different parts of its domain.

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How do you determine the value of a piece-wise function at a specific point?

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To determine the value of a piece-wise function at a specific point, identify which interval the point falls into and use the corresponding expression for that interval.

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What is the domain of a piece-wise function?

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The domain of a piece-wise function is the set of all input values (x-values) for which the function is defined, often specified in intervals.

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What is the range of a piece-wise function?

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

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How do you graph a piece-wise function?

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To graph a piece-wise function, plot each piece of the function according to its defined interval, ensuring to use open or closed dots as appropriate for the endpoints.

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What does it mean for a piece-wise function to be continuous?

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

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What is a common example of a piece-wise function?

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What is the significance of the endpoints in piece-wise functions?

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Endpoints determine whether the function includes or excludes certain values, indicated by closed (included) or open (excluded) dots on the graph.

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How do you write a piece-wise function?

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A piece-wise function is written using braces to group the different expressions, each associated with its respective interval.

Front

What is the difference between a closed interval and an open interval?

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A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).