ALG1H 4.7 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 evaluate a piecewise function at a specific point?

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To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and then use the corresponding expression to find the value.

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CCSS.HSF.IF.A.2

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What does f(0) = 4 indicate in a piecewise function?

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It indicates that when the input (x) is 0, the output (f(0)) is 4, based on the definition of the function at that point.

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CCSS.HSF.IF.A.2

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If f(2) = 1, what does this tell us about the function at x = 2?

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It tells us that when the input (x) is 2, the output (f(2)) is 1, indicating the value of the function at that specific point.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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What is the significance of finding f(-2) = 8 in a piecewise function?

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It shows that for the input (x) of -2, the output (f(-2)) is 8, which is determined by the relevant piece of the function.

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CCSS.HSF.IF.A.2

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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 and ensure to use open or closed circles to indicate whether endpoints are included.

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CCSS.HSF-IF.C.7B

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What is 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, which may vary across different pieces.

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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 (f(x)) that the function can produce, depending on the defined pieces.

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CCSS.HSF-IF.C.7B

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What does it mean if a piecewise function has a discontinuity?

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A discontinuity in a piecewise function means there is a break or jump in the graph, indicating that the function is not continuous at that point.

Tags

CCSS.HSF-IF.C.7B

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How do you determine if a piecewise function is continuous at a point?

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A piecewise function is continuous at a point if the limit from the left equals the limit from the right and both equal the function's value at that point.