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 at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

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

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 over its domain.

Front

How can you identify the intervals of a piecewise function?

Back

Intervals of a piecewise function can be identified by examining the conditions or inequalities that define each piece.

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 is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the function includes or excludes certain values in its domain, affecting continuity and the function's graph.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and use open or closed circles to indicate whether endpoints are included.

Front

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

Back

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

Front

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

Back

Substitute the specific point into the appropriate piece of the function based on its defined interval.