ALG1H 4.7 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 parts of its domain.

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How do you evaluate a piecewise function?

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To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that expression to find the output.

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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 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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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 value of f(x) for a piecewise function?

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You find f(x) by substituting x into the appropriate piece of the function based on the defined intervals.

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What is a graph of a piecewise function?

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A graph of a piecewise function consists of multiple segments, each representing a different expression of the function over specific intervals.

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What does 'x ≥ 0' mean in the context of a piecewise function?

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'x ≥ 0' indicates that the piece of the function applies to all x-values that are 0 or greater.

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How do you determine the domain restrictions of a piecewise function?

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Domain restrictions are determined by the conditions specified for each piece of the function, indicating where each piece is valid.

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What is the significance of the output value in a piecewise function?

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The output value indicates the result of the function for a specific input, which can vary depending on the piece of the function being used.