Piecewise & Absolute Value 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 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 in which the input value falls 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 absolute value of a number?

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The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

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CCSS.6.NS.C.7C

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How do you graph an absolute value function?

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An absolute value function has a V-shape graph. The vertex is at the point where the expression inside the absolute value equals zero.

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CCSS.HSF-IF.C.7D

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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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Given f(x) = |x|, what is f(-3)?

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f(-3) = 3.

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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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How do you find the maximum value of a piecewise function?

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To find the maximum value, evaluate the function at the endpoints of the intervals and at any critical points within the intervals.

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CCSS.HSF-IF.C.7B

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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.

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CCSS.HSF-IF.C.7B

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How do you solve an absolute value equation?

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To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case.