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 input values (x-values) for which the function is defined, often represented as intervals.

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What does 'DNE' stand for in the context of functions?

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DNE stands for 'Does Not Exist', indicating that a function value is not defined for a particular input.

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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 based on whether the endpoints are included.

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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 output values (y-values) that the function can produce, based on its defined pieces.

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What is the significance of the endpoints in piecewise functions?

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Endpoints in piecewise functions determine whether the function includes or excludes certain values, affecting the continuity and graph of the function.

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How do you determine the number of pieces in a piecewise function?

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The number of pieces in a piecewise function is determined by the number of different expressions or formulas used to define the function over its domain.

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What is an example of a piecewise function?

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An example of a piecewise function is: f(x) = { x^2 for x < 0; 2x + 1 for x ≥ 0 }.

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What is the importance of matching graphs with equations in piecewise functions?

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Matching graphs with equations helps to visually understand how the function behaves in different intervals and confirms the accuracy of the piecewise definition.