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 parts of its domain.

Front

What does the domain of a function represent?

Back

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

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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 graph of a piecewise function?

Back

A graph of a piecewise function consists of multiple segments, each representing a different expression for specific intervals of the domain.

Front

How do you evaluate a piecewise function at a given x-value?

Back

To evaluate a piecewise function at a given x-value, determine which piece of the function applies to that x-value and use the corresponding expression.

Front

What is the significance of the endpoints in piecewise functions?

Back

Endpoints in piecewise functions indicate where one piece of the function ends and another begins, often determining whether the endpoint is included or excluded.

Front

What is the difference between open and closed intervals?

Back

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

Front

How can you identify the pieces of a piecewise function from its graph?

Back

You can identify the pieces of a piecewise function from its graph by observing the different segments and their corresponding x-value intervals.