Piecewise Functions

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What is a piecewise function?

Back

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 determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which piece of the function applies to that point based on its domain restrictions.

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What is the domain of a function?

Back

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 defined at a point?

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A function is defined at a point if there is a corresponding output value (y-value) for that input value (x-value).

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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 domain restrictions for a piece of a piecewise function?

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To find the domain restrictions for a piece of a piecewise function, analyze the conditions under which that piece is valid based on its definition.

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What is the significance of the notation 'f(x) = ...' in piecewise functions?

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The notation 'f(x) = ...' indicates the output value of the function f for a given input x, which may depend on the piece of the function being used.

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What is the difference between '>' and '≥' in domain restrictions?

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'>' means that the value is not included in the domain (open interval), while '≥' means that the value is included (closed interval).

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How do 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, using open or closed dots as appropriate.

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What is a constant function in the context of piecewise functions?

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A constant function is a piece of a piecewise function that has the same output value for all input values in its domain.