4.7 Graphing 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 over 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 does the notation f(x) = { expression1 if condition1; expression2 if condition2 } mean?

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This notation defines a piecewise function where different expressions are used based on the conditions specified.

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How can you graph a piecewise function?

Back

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.

Front

What is the significance of the domain in a piecewise function?

Back

The domain of a piecewise function specifies the intervals over which each piece of the function is valid.

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How do you determine the number of pieces in a piecewise function?

Back

The number of pieces in a piecewise function is determined by the number of different expressions or formulas defined for different intervals.

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What is the importance of continuity in piecewise functions?

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Continuity in piecewise functions is important because it affects the function's behavior and whether it can be graphed smoothly without breaks.

Front

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

Back

To find the value of f(x) for a piecewise function, identify the interval that contains x and apply the corresponding expression.

Front

What does it mean for a function to be increasing or decreasing on an interval?

Back

A function is increasing on an interval if its output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

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How can you identify the fastest moving interval in a piecewise function representing speed?

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To identify the fastest moving interval, look for the interval where the function has the highest slope or rate of change.