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 over different intervals of its domain.

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How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering the intervals where each piece is defined.

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What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) for open intervals and [a, b] for closed intervals.

Front

What does the notation (a, b) mean?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

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What does the notation [a, b] mean?

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The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

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How do you find the range of a piecewise function?

Back

To find the range, evaluate the outputs of each piece of the function over its domain and determine the set of all possible output values.

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What is the significance of the endpoints in piecewise functions?

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Endpoints determine whether the values at those points are included in the function (closed interval) or not (open interval).

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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, identify which piece of the function corresponds to that point's domain and use the appropriate formula.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

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What is a discontinuous piecewise function?

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A discontinuous piecewise function has at least one point where the function is not continuous, meaning there is a jump or break in the graph.