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 use the corresponding expression to find the function's value.

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What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, often specified by the intervals in the function's definition.

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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, based on the defined pieces.

Front

Evaluate f(-3) for the piecewise function: f(x) = { x + 2, x < -1; -3x, -1 ≤ x < 2; 4, x ≥ 2 }

Back

f(-3) = -1.

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Evaluate f(0) for the piecewise function: f(x) = { x + 2, x < -1; -3x, -1 ≤ x < 2; 4, x ≥ 2 }

Back

f(0) = 4.

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Evaluate h(5) for the piecewise function: h(x) = { -x^2, x < 0; 3x + 2, 0 ≤ x < 5; 7, x ≥ 5 }

Back

h(5) = 7.

Front

What is the importance of continuity in piecewise functions?

Back

Continuity in piecewise functions ensures that there are no jumps or breaks in the graph, which is important for certain applications like calculus.

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What does it mean for a piecewise function to be defined at a point?

Back

A piecewise function is defined at a point if there is a specific expression that applies to that point based on its interval.

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How can 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 circles to indicate whether endpoints are included.