Piecewise Functions

Front

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.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval that contains the input value and use the corresponding expression to find the output.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all input values for which the function is defined, which may vary across different pieces.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values that the function can produce.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots as appropriate.

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

Back

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

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).

Front

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

Back

To find f(x), determine which piece of the function applies to the given x value and substitute x into that piece.

Front

What is a common mistake when working with piecewise functions?

Back

A common mistake is to use the wrong expression for a given input value, often due to misidentifying the interval.

Front

What is the significance of the endpoints in piecewise functions?

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Endpoints determine whether the function includes or excludes certain values, affecting continuity and the graph.