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.

Tags

CCSS.HSF-IF.C.7B

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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 interval the point falls into and then use the corresponding expression for that interval.

Tags

CCSS.HSF.IF.A.2

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What is the domain of a function?

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The domain of a 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 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 find the domain of a piecewise function?

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To find the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

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What does it mean for a function to be continuous?

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A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the notation f(x) in piecewise functions?

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The notation f(x) represents the output of the function for a given input x, and it indicates which piece of the function to use based on the value of x.

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How do you determine the output of a piecewise function at a boundary point?

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At a boundary point, check the definition of the function to see if the point is included in the interval (using ≤ or <) and use the appropriate expression.

Tags

CCSS.HSF.IF.A.2

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What is the graphical representation of a piecewise function?

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The graphical representation of a piecewise function consists of different line segments or curves that correspond to the different pieces of the function, each defined over specific intervals.

Tags

CCSS.HSF-IF.C.7B

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What is the importance of understanding piecewise functions in real-world applications?

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Understanding piecewise functions is important in real-world applications because they can model situations where a quantity changes based on different conditions or ranges.