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, identify the interval in which the input value falls and use the corresponding expression to find the output.

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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 input values for which the function is defined, which may vary across different pieces.

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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 that the function can produce.

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How do 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 does f(3) = -1 indicate in a piecewise function?

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It indicates that when the input value is 3, the output value of the function is -1, based on the specific piece of the function that applies.

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What does f(0) = -6 indicate in a piecewise function?

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It indicates that when the input value is 0, the output value of the function is -6, based on the specific piece of the function that applies.

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What is the significance of matching a piecewise function to a graph?

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Matching a piecewise function to a graph helps to visualize how the function behaves across different intervals and to understand its overall shape.

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What is f(-2) = -4 in a piecewise function?

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It indicates that when the input value is -2, the output value of the function is -4, based on the specific piece of the function that applies.

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What is an example of a piecewise function?

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An example of a piecewise function is: f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 }.