Piecewise Practice

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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 for that interval.

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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.

Front

How do you find the value of f(x) for x in a piecewise function?

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Identify the interval that contains x, then apply the formula associated with that interval to find f(x).

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What is the formula for calculating earnings in a piecewise rate scenario?

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The earnings can be calculated by applying the appropriate hourly rate for each segment of hours worked, summing the total for all segments.

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How do 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.

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What does it mean if a piecewise function has a discontinuity?

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A discontinuity in a piecewise function means that there is a jump or break in the graph, indicating that the function does not have a defined value at that point.

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How can you determine if a piecewise function is continuous?

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A piecewise function is continuous if the limits from both sides of a point match the function's value at that point.

Front

What is the importance of endpoints in piecewise functions?

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Endpoints determine whether the function includes or excludes certain values, affecting the overall behavior and continuity of the function.

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How do you calculate the total cost in a piecewise pricing model?

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To calculate the total cost, apply the pricing rules for each segment of usage and sum the costs for all segments.