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.

Front

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?

Back

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