2.4 Evaluating 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

To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

Front

What does the notation (-∞, -1] U [3, +∞) represent?

Back

This notation represents the domain of a function that includes all real numbers less than or equal to -1 and all real numbers greater than or equal to 3.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and use the corresponding expression.

Front

What is the significance of the graph of a piecewise function?

Back

The graph visually represents the different pieces of the function and how they connect or transition at specific points.

Front

What does f(-3) = -3 indicate about the function?

Back

It indicates that when the input is -3, the output of the function is -3, showing a specific point on the graph.

Front

What is the difference between closed and open intervals in domain?

Back

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

Front

How can you identify the correct graph of a piecewise function?

Back

To identify the correct graph, analyze the function's pieces and their respective domains, then match them to the graph that accurately represents those pieces.

Front

What does the notation 1 ≤ x ≤ 4 mean?

Back

This notation means that x can take any value from 1 to 4, including both endpoints.

Front

How do you find f(-2) in a piecewise function?

Back

To find f(-2), determine which piece of the function applies when x = -2 and use that expression to calculate the output.