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 determine the domain of a piecewise function?

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To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

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What does the notation f(x) mean in a piecewise function?

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f(x) represents the output of the function for a given input x, which may depend on which piece of the function is applicable.

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What is the significance of the domain in piecewise functions?

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The domain indicates the set of input values for which the function is defined, which is crucial for understanding the behavior of the function.

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How do you graph a piecewise function?

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To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots based on the inclusion of endpoints.

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What is the difference between open and closed intervals?

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

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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, which can be determined by evaluating each piece of the function.

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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 use the corresponding expression.

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What is a discontinuity in a piecewise function?

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A discontinuity occurs when there is a sudden jump or break in the graph of the function, often at the boundaries of the pieces.

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How can you identify the domain restrictions of a piecewise function?

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Domain restrictions can be identified by analyzing the conditions under which each piece of the function is defined.