Piecewise Functions

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What is a piecewise function?

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A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

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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, identify the interval that the input value falls into and use the corresponding expression to find the output.

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CCSS.HSF.IF.A.2

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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-values) for which the function is defined.

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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.

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 of the function according to its defined interval, ensuring to use open or closed dots as appropriate.

Tags

CCSS.HSF-IF.C.7B

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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 at the points where the pieces meet.

Tags

CCSS.HSF-IF.C.7B

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

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

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CCSS.6.EE.B.8

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How do you find the value of g(7) in a piecewise function?

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To find g(7), determine which piece of the function applies when x = 7 and substitute 7 into that expression.

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CCSS.HSF.IF.A.2

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If f(x) = { 2x + 1 for x < 0; 3 for x = 0; x^2 for x > 0 }, what is f(0)?

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f(0) = 3.

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CCSS.HSF.IF.A.2

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If you have $75 and the cost to rent a Karaoke machine is $37.50 per day, how many days can you rent it?

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You can rent the Karaoke machine for 2 days.

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CCSS.6.EE.B.7