Piecewise Functions

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What is a piecewise function?

Back

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

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, 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 input values for which the function is defined, which may vary across different pieces.

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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, which can also vary depending on the piece being evaluated.

Tags

CCSS.HSF-IF.C.7B

Front

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

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f(-3) = 9, since -3 falls in the interval x < 0.

Tags

CCSS.HSF.IF.A.2

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

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f(2) = 4, since 2 falls in the interval x >= 1.

Tags

CCSS.HSF.IF.A.2

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What is the importance of the 'break' in a piecewise function?

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The 'break' indicates where the function changes its rule or formula, which is crucial for understanding its behavior.

Tags

CCSS.HSF-IF.C.7B

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How can piecewise functions be graphed?

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Piecewise functions can be graphed by plotting each piece separately over its defined interval and ensuring continuity where applicable.

Tags

CCSS.HSF-IF.C.7B

Front

What is a common application of piecewise functions?

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Piecewise functions are commonly used in real-world scenarios, such as tax brackets, shipping costs, and rental rates.

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If a piecewise function has a discontinuity, what does that mean?

Back

A discontinuity in a piecewise function means there is a 'jump' or 'break' in the graph where the function is not continuous.

Tags

CCSS.HSF-IF.C.7B