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

How do 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 domain of a piecewise function?

Back

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

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, meaning it can be drawn without lifting the pencil.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all output values (y-values) that the function can produce, which may vary depending on the pieces.

Front

How do you determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which piece of the function applies to that input value and use the corresponding formula.

Front

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

Back

Endpoints in a piecewise function indicate whether the function includes or excludes certain values, affecting the continuity and domain.

Front

How can you identify the domain restrictions of a piecewise function?

Back

Domain restrictions can be identified by examining the intervals defined for each piece of the function and noting any conditions that limit the input values.

Front

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

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

Back

To find f(x) for a given x, locate the appropriate piece of the function that corresponds to the value of x and apply the formula.