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 then use the corresponding expression for that interval.

Tags

CCSS.HSF.IF.A.2

Front

What does the notation f(x) = { expression1 if condition1; expression2 if condition2 } represent?

Back

This notation represents a piecewise function where different expressions are used based on the conditions specified.

Front

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

Back

The domain of a piecewise function specifies the input values for which the function is defined, and it may vary for different pieces of the function.

Tags

CCSS.HSF-IF.C.7B

Front

How can 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.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Tags

CCSS.HSF-IF.C.7B

Front

How do you find the range of a piecewise function?

Back

To find the range of a piecewise function, evaluate the outputs of each piece over its domain and combine the results.

Front

What is a continuous piecewise function?

Back

A continuous piecewise function is one where there are no breaks or jumps in the graph, meaning the function values match at the endpoints of the intervals.

Tags

CCSS.HSF-IF.C.7B

Front

What is a discontinuous piecewise function?

Back

A discontinuous piecewise function has breaks or jumps in the graph, indicating that the function values do not match at the endpoints of the intervals.

Tags

CCSS.HSF-IF.C.7B

Front

How do you determine the number of pieces in a piecewise function?

Back

The number of pieces in a piecewise function is determined by the number of different expressions or formulas defined for different intervals.

Tags

CCSS.HSF-IF.C.7B