Piecewise Function

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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

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What is a step function?

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A step function is a type of piecewise function that has a graph resembling a series of steps, where the function value remains constant within certain intervals.

Tags

CCSS.HSF-IF.C.7B

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How do you evaluate a piecewise function?

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To evaluate a piecewise function, determine which interval the input value falls into and then use the corresponding expression to find the output.

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CCSS.HSF.IF.A.2

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What is the significance of the domain in piecewise functions?

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The domain of a piecewise function specifies the input values for which each piece of the function is defined.

Tags

CCSS.HSF-IF.C.7B

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If f(x) = { x + 2 for x < 0; x^2 for x >= 0 }, what is f(-1)?

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f(-1) = -1 + 2 = 1.

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CCSS.HSF.IF.A.2

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If f(x) = { 3x for x < 1; 2x + 1 for x >= 1 }, what is f(2)?

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f(2) = 2(2) + 1 = 5.

Tags

CCSS.HSF.IF.A.2

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What is the output of a step function when the input is at a boundary?

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The output at a boundary can depend on whether the function is defined to include that boundary (closed interval) or not (open interval).

Tags

CCSS.HSF-IF.C.7B

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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, ensuring to use open or closed dots as appropriate for boundaries.

Tags

CCSS.HSF-IF.C.7B

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What is the value of f(0) if f(x) = { -3 for x < 0; 4 for x >= 0 }?

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f(0) = 4.

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CCSS.HSF.IF.A.2

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What is the value of g(7) if g(x) = { 2x - 1 for x < 5; 3x + 2 for x >= 5 }?

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g(7) = 3(7) + 2 = 23.