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.

Tags

CCSS.HSF-IF.C.7B

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How do you determine the domain of a piecewise function?

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The domain of a piecewise function is the set of all possible input values (x) for which the function is defined, often determined by the intervals specified in the function.

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What does the notation f(x) mean?

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f(x) represents the value of the function f at the input x.

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CCSS.HSF.IF.A.2

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What is the range of a function?

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

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How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which interval the input value falls into and use the corresponding expression to find the output.

Tags

CCSS.HSF.IF.A.2

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What is the significance of the notation '≤' in a domain interval?

Back

The notation '≤' indicates that the endpoint is included in the interval, meaning the value at that point is part of the domain.

Tags

CCSS.HSF.IF.B.5

CCSS.8.F.A.1

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What is the significance of the notation '<' in a domain interval?

Back

The notation '<' indicates that the endpoint is not included in the interval, meaning the value at that point is not part of the domain.

Tags

CCSS.HSF.IF.B.5

CCSS.8.F.A.1

Front

If f(x) = 3 for x > 2, what does this mean?

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This means that for any value of x greater than 2, the output of the function f will always be 3.

Tags

CCSS.HSF.LE.B.5

Front

What is the difference between domain and range?

Back

Domain refers to the set of input values (x) for which the function is defined, while range refers to the set of output values (y) that the function can produce.

Tags

CCSS.HSF.IF.A.1

CCSS.8.F.A.1

Front

How can you graph a piecewise function?

Back

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 the inclusion of endpoints.

Tags

CCSS.HSF-IF.C.7B