Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

How do you determine the range of a piecewise function?

Back

To determine the range, evaluate the output values of the function for each piece and identify the overall set of possible outputs.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you find the domain of a piecewise function?

Back

To find the domain, identify the x-values for which each piece of the function is defined and combine them.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is a discontinuity in a piecewise function?

Back

A discontinuity is a point where the function is not continuous, often occurring at the boundaries between pieces.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate, determine which piece of the function applies to the given input value and use that expression.

Front

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

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

What is a step function?

Back

A step function is a type of piecewise function that has a constant value within each interval and jumps to a different value at the boundaries.

Front

How can you graph a piecewise function?

Back

To graph, plot each piece of the function according to its defined interval and connect the points appropriately.