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 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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What does the notation f(x) = { expression1 if condition1; expression2 if condition2 } represent?

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This notation represents a piecewise function where different expressions are used based on the conditions specified.

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

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The domain of a piecewise function specifies the input values for which the function is defined, and it may vary for different pieces of the function.

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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.

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What is the difference between open and closed intervals in piecewise functions?

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Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

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How do you find the range of a piecewise function?

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To find the range of a piecewise function, evaluate the outputs of each piece over its domain and combine the results.

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What is a continuous piecewise function?

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A continuous piecewise function is one where there are no breaks or jumps in the graph, meaning the function values match at the endpoints of the intervals.

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What is a discontinuous piecewise function?

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A discontinuous piecewise function has breaks or jumps in the graph, indicating that the function values do not match at the endpoints of the intervals.

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How do you determine the number of pieces in a piecewise function?

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The number of pieces in a piecewise function is determined by the number of different expressions or formulas defined for different intervals.