Quick Flashcard - Piecewise Defined Functions

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What is a piecewise-defined function?

Back

A piecewise-defined 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-defined function at a specific point?

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To evaluate a piecewise-defined function at a specific point, determine which interval the point falls into and then 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 find the domain of a piecewise-defined function?

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

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What does it mean for a function to be continuous?

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A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

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

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Endpoints in a piecewise-defined function indicate where the function changes from one expression to another, and they can be included or excluded from the domain.

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How do you graph a piecewise-defined function?

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To graph a piecewise-defined function, plot each piece of the function on its respective interval, paying attention to whether endpoints are included or excluded.

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What is the formula for Lea's weekly pay if she works more than 40 hours?

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If Lea works more than 40 hours, her weekly pay is given by P(h) = 10.5h - 140, where h is the total hours worked.

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What is the formula for Lea's weekly pay if she works 40 hours or less?

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If Lea works 40 hours or less, her weekly pay is given by P(h) = 7h.