5.8.1 Evaluating 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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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 to find the function's value.

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What is the domain of a function?

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

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What is the range of a function?

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

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How do you determine which equation to use in a piecewise function?

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To determine which equation to use, identify the input value and find the corresponding interval in the piecewise definition.

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What is the significance of the 'top', 'middle', and 'bottom' labels in piecewise functions?

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These labels refer to the different expressions used in the piecewise function for different intervals of the input.

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How do you graph a piecewise function?

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