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?

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To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

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What is the domain of a piecewise function?

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The domain of a piecewise 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 piecewise function?

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

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What does it mean for a piecewise function to be continuous?

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

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What is the significance of the 'if' statements in piecewise functions?

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The 'if' statements in piecewise functions specify the conditions under which each piece of the function applies.

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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 and connect them appropriately.

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

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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)).

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How do you find the value of a piecewise function at a specific point?

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To find the value of a piecewise function at a specific point, determine which piece of the function applies to that point and evaluate it.

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What is a common mistake when working with piecewise functions?

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A common mistake is to use the wrong expression for a given input value, often due to misidentifying the interval.