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 is the significance of the domain in piecewise functions?

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The domain of a piecewise function specifies the intervals over which each piece of the function is defined, which is crucial for determining the function's behavior.

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What does it mean for a piecewise function to be continuous?

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A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces meet.

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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 circles to indicate whether endpoints are included.

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What is the difference between open and closed intervals in piecewise functions?

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Open intervals do not include their endpoints, while closed intervals do include their endpoints, affecting the function's continuity and values at those points.

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How do you find the limit of a piecewise function at a point?

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To find the limit of a piecewise function at a point, evaluate the function from both sides of the point and check if the limits agree.

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What is the role of the 'if' statement in piecewise functions?

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The 'if' statement in piecewise functions specifies the conditions under which each piece of the function applies.

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How do you determine the range of a piecewise function?

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To determine the range of a piecewise function, evaluate each piece over its interval and combine the resulting values.

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What is a common application of piecewise functions in real life?

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Piecewise functions are commonly used to model situations where a quantity changes based on different conditions, such as tax brackets or shipping costs.