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 intervals 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 interval the input value falls into and use the corresponding expression to find the output.

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What does 'undefined' mean in the context of a function?

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'Undefined' means that the function does not have a valid output for a given input, often due to division by zero or an input not falling within the function's domain.

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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 possible input values (x-values) for which the function is defined.

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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 (y-values) that the function can produce.

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How can you graph a piecewise function?

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

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What is a continuous piecewise function?

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A continuous piecewise function is one where the pieces connect without any breaks or jumps at the boundaries of the intervals.

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What is a discontinuous piecewise function?

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A discontinuous piecewise function has breaks or jumps in its graph, meaning it is not continuous at certain points.

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How do you find the value of f(x) for x = -2 in a piecewise function?

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Identify the interval that includes x = -2 and use the corresponding expression to calculate f(-2).

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What does it mean if a piecewise function has multiple pieces?

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It means that the function is defined by different rules or formulas for different segments of its domain.