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 parts 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 correct piece of the function that corresponds to the input value and then compute the output using that piece.

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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 does it mean for a function to be undefined at a certain point?

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A function is undefined at a certain point if there is no output value (y-value) corresponding to that input value (x-value) in the function's definition.

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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 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, substitute the point into the appropriate piece of the function based on its domain.

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What is a domain restriction in a piecewise function?

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A domain restriction in a piecewise function specifies the values of x for which a particular piece of the function is valid.

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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 domain restrictions and connect the points appropriately.

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What is the difference between continuous and discontinuous piecewise functions?

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A continuous piecewise function has no breaks or gaps in its graph, while a discontinuous piecewise function has breaks or jumps at certain points.