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 intervals 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 interval the point falls into and use the corresponding expression.

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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 is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the domain of a piecewise function?

Back

To find the domain of a piecewise function, consider the domains of each piece and combine them, ensuring all intervals are included.

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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 does not have a value at a certain point.

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What is the significance of closed and open intervals in piecewise functions?

Back

Closed intervals include their endpoints, while open intervals do not. This affects whether the function includes or excludes certain values.

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How can you graph a piecewise function?

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To graph a piecewise function, plot each piece according to its defined interval and use solid dots for closed intervals and open dots for open intervals.

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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.

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What is a discontinuity in a piecewise function?

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A discontinuity occurs when there is a break or jump in the graph of the function, often at the boundaries of the pieces.