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.

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.

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)).

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.

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.

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.

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.