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.

Tags

CCSS.HSF-IF.C.7B

Front

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 then use the corresponding expression to find the function's value.

Tags

CCSS.HSF.IF.A.2

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all input values (x-values) for which the function is defined, often specified by the intervals in the piecewise 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, based on its defined pieces.

Tags

CCSS.HSF-IF.C.7B

Front

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 as appropriate for endpoints.

Tags

CCSS.HSF-IF.C.7B

Front

What does it mean for a piecewise function to be continuous?

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A piecewise function is continuous if there are no breaks, jumps, or holes in the graph, meaning the function's value approaches the same limit from both sides at the endpoints of the intervals.

Tags

CCSS.HSF-IF.C.7B

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints (e.g., (a, b)), while a closed interval includes its endpoints (e.g., [a, b]).

Tags

CCSS.6.EE.B.8

Front

How do you find the value of f(x) for x in a piecewise function?

Back

To find f(x) for a given x, identify the interval that x belongs to and apply the corresponding function rule.

Tags

CCSS.HSF.IF.A.2

Front

What is a common mistake when working with piecewise functions?

Back

A common mistake is to use the wrong piece of the function for a given x-value, often due to misidentifying the interval.

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of the endpoints in piecewise functions?

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

Tags

CCSS.HSF-IF.C.7B