Piecewise Functions

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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 intervals of its domain.

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

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression to find the function's value.

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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 on its respective interval, ensuring to use open or closed dots based on whether the endpoints are included.

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What does 'f(x) = -x + 4 if x < 2' represent?

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This represents a linear function with a negative slope that applies to x-values less than 2.

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What does 'f(x) = 2x - 6 if x ≥ 2' represent?

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This represents a linear function with a positive slope that applies to x-values greater than or equal to 2.

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What is the significance of the point where the pieces of a piecewise function meet?

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The point where the pieces meet is called a breakpoint, and it is important for determining continuity and the overall behavior of the function.

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How do you determine if a piecewise function is continuous?

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A piecewise function is continuous if the limit from the left and the limit from the right at the breakpoint are equal to the function's value at that point.

Front

What is an example of a piecewise function?

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An example is: f(x) = { x^2 for x < 0; 2x + 1 for x ≥ 0 }.