Algebra 3 Flashcard- 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 at a specific point?

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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 does it mean if a piecewise function is undefined at a certain point?

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If a piecewise function is undefined at a certain point, it means that there is no corresponding output value for that input in the function's definition.

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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 circles to indicate whether endpoints are included.

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What is the significance of the endpoints in piecewise functions?

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Endpoints in piecewise functions determine whether the function includes or excludes certain values, affecting the continuity and behavior of the graph.

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How do you find the value of f(x) for x in a specific interval?

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To find f(x) for x in a specific interval, identify the correct piece of the function that corresponds to that interval and substitute x into that expression.

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What is the difference between continuous and discontinuous piecewise functions?

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Continuous piecewise functions have no breaks in their graphs, while discontinuous piecewise functions have gaps or jumps at certain points.

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How do you determine if a piecewise function is increasing or decreasing?

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To determine if a piecewise function is increasing or decreasing, analyze the slopes of the linear pieces or the behavior of the function in each interval.

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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 (x-values) for which the function is defined, which may vary across different pieces.

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How do you find the range of a piecewise function?

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To find the range of a piecewise function, evaluate the outputs (y-values) for each piece and combine them to determine all possible output values.