Piece-Wise Functions REVIEW

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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 parts of its domain.

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How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which part 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 piecewise function?

Back

The domain of a piecewise function is the set of all input values for which the function is defined, often specified in the function's definition.

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What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces connect.

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What is the difference between open and closed intervals in piecewise functions?

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Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

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How do you graph a piecewise function?

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To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed dots as appropriate.

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What is the significance of the slope in a linear piecewise function?

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The slope in a linear piecewise function indicates the rate of change of the function within that interval.

Front

How do you find the value of f(x) for a piecewise function?

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To find f(x), identify the interval in which x falls and use the corresponding expression to calculate the output.

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What is a common mistake when working with piecewise functions?

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A common mistake is to use the wrong expression for a given input value, often due to misidentifying the interval.

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What is the notation for piecewise functions?

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Piecewise functions are often written using curly braces to indicate different cases, e.g., f(x) = { expression1 for condition1, expression2 for condition2 }.