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 determine the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, considering the conditions for each piece.

Front

What does the notation f(x) = { x if x < 4; -x + 1 if x ≥ 4 mean?

Back

This notation means that for x values less than 4, the function f(x) equals x, and for x values greater than or equal to 4, f(x) equals -x + 1.

Front

How do you evaluate a piecewise function at a specific point, such as f(2)?

Back

To evaluate f(2), determine which piece of the function applies when x = 2, then substitute 2 into that expression.

Tags

CCSS.HSF.IF.A.2

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce based on its defined pieces.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

Closed intervals include their endpoints (e.g., [1, 4]), while open intervals do not include their endpoints (e.g., (1, 4)).

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 solid dots for closed intervals and open dots for open intervals.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

Breakpoints are the x-values where the function changes from one expression to another, and they are crucial for determining the function's behavior.

Tags

CCSS.HSF-IF.C.7B

Front

How do you match a graph to its corresponding piecewise function?

Back

To match a graph to its piecewise function, analyze the graph's segments and their slopes, intercepts, and endpoints, then compare these characteristics to the function's definitions.

Tags

CCSS.HSF-IF.C.7B

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 pieces connect at their endpoints.

Tags

CCSS.HSF-IF.C.7B