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 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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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 dots as appropriate.

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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 the graph at the points where the pieces meet.

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

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Endpoints determine whether the function includes or excludes certain values in its domain, affecting the continuity and graph.

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

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Substitute the specific point into the appropriate piece of the function based on its defined intervals.

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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 endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).

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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.