Piecewise and Step 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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What is a step function?

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A step function is a piecewise constant function that jumps from one value to another without taking on any values in between.

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CCSS.HSF-IF.C.7B

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How do you identify a piecewise function from a graph?

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You can identify a piecewise function from a graph by looking for distinct segments or pieces that correspond to different intervals of the x-axis.

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CCSS.HSF-IF.C.7B

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What is the absolute value function?

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The absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|.

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CCSS.HSF-IF.C.7D

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What is the general form of a piecewise function?

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The general form of a piecewise function is f(x) = { expression1 for x in interval1, expression2 for x in interval2, ... }.

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What is 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 or segment of the function.

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How do you evaluate a piecewise function at a given point?

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To evaluate a piecewise function at a given point, determine which interval the point falls into and use the corresponding expression.

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CCSS.HSF.IF.A.2

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What is a common application of step functions?

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Step functions are commonly used in real-life scenarios such as tax brackets, shipping costs, and utility rates.

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CCSS.7.EE.A.1

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What is the difference between continuous and discontinuous piecewise functions?

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Continuous piecewise functions have no breaks or jumps in their graphs, while discontinuous piecewise functions have breaks or jumps at certain points.

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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 and connect the points appropriately.

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CCSS.HSF-IF.C.7B