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 determine the value of a piecewise function at a specific point?

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To determine the value of a piecewise function at a specific point, identify which piece of the function applies to that point based on its domain restrictions.

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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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How do you graph a piecewise function?

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To graph a piecewise function, graph each piece of the function on its specified interval, ensuring to use open or closed dots as appropriate.

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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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What is the significance of the 'if' statement in piecewise functions?

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The 'if' statement in piecewise functions specifies the conditions under which each piece of the function is applicable.

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How do you find the intersection of two piecewise functions?

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To find the intersection of two piecewise functions, set the two functions equal to each other and solve for x within the relevant domains.

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What is a domain restriction?

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A domain restriction is a limitation on the input values for which a function is defined, often specified in piecewise functions.

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

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To evaluate a piecewise function at a boundary point, check both pieces of the function to see which one applies at that point.