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 determine the domain of a piecewise function?

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The domain of a piecewise function is the union of the domains of each piece, considering any restrictions from the individual pieces.

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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-values) that the function can produce.

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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, identify which interval the point falls into and use the corresponding expression for that interval.

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CCSS.HSF.IF.A.2

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What does it mean if a function is defined for all real numbers?

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If a function is defined for all real numbers, it means that there are no restrictions on the input values (x-values) for the function.

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CCSS.HSF.IF.A.1

CCSS.8.F.A.1

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What is the significance of the range being y ≤ 4?

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If the range is y ≤ 4, it means that the output values of the function can be any number less than or equal to 4.

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CCSS.HSF.IF.B.5

CCSS.8.F.A.1

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How do you calculate earnings based on a piecewise rate?

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To calculate earnings based on a piecewise rate, apply the appropriate rate to each segment of hours worked and sum the total earnings.

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What is the formula for calculating the total cost in a piecewise function?

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The total cost in a piecewise function is calculated by applying the cost formula for each segment of the input and summing the results.

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What is the importance of understanding the domain and range in piecewise functions?

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Understanding the domain and range helps in determining the valid input and output values for the function, which is crucial for graphing and solving problems.

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 on its respective interval and ensure to indicate open or closed endpoints as necessary.

Tags

CCSS.HSF-IF.C.7B