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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.HSF.IF.A.2