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Shown is a graph of y=f(x) a. find and state the domain f in interval notation. b. find and state the range of f in interval notation.

Shown is a graph of y=f(x) a. find and state the domain f in interval notation. b. find and state the range of f in interval notation.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Shown is a graph of y=f(x) a. find and state the domain f in interval notation. b. find and state the range of f in interval notation.
### Piecewise Function Graph Explanation This graph represents a piecewise function defined on the Cartesian coordinate plane. The x-axis and y-axis are labeled accordingly, with units marked at regular intervals. The graph is divided into two distinct segments, both featuring linear components. #### Graph Components 1. **First Segment:** - **Points:** - Starts from (-3, -2) - Ends at (0,1) and includes the point (0,1) depicted by a solid dot. - **Line:** - The solid line connects the points (-3, -2) and (0, 1). - The point (-1, 0) is indicated with a hollow circle, showing that the function does not include this point. - **Behavior:** - This segment represents an increasing linear function from (-3, -2) to (0,1), excluding (-1,0). 2. **Second Segment:** - **Points:** - Starts from (1, 3) and includes the point (1,3) depicted by a hollow circle. - Ends at (3, -1) - **Line:** - The solid line connects the points (1, 3) and (3, -1). - **Behavior:** - This segment represents a decreasing linear function from (1, 3) to (3, -1). #### Interpretation - **Hollow Circles:** Indicate that the function is not defined at these particular points. - **Solid Dots:** Indicate that the function is defined at these points. ### Summary This piecewise function has two parts, separated at x-values -1 and 1, each representing a different linear behavior. The first segment increases from (-3, -2) to (0,1), excluding (-1,0), and the second segment decreases from (1, 3) to (3, -1), excluding (1,3). ### Educational Website Context This graph of a piecewise function is useful for demonstrating how functions can behave differently over different segments of their domain. Understanding piecewise functions is essential for grasping more complex functions and for solving real-world problems where functions may change behavior across different intervals.
Transcribed Image Text:### Piecewise Function Graph Explanation This graph represents a piecewise function defined on the Cartesian coordinate plane. The x-axis and y-axis are labeled accordingly, with units marked at regular intervals. The graph is divided into two distinct segments, both featuring linear components. #### Graph Components 1. **First Segment:** - **Points:** - Starts from (-3, -2) - Ends at (0,1) and includes the point (0,1) depicted by a solid dot. - **Line:** - The solid line connects the points (-3, -2) and (0, 1). - The point (-1, 0) is indicated with a hollow circle, showing that the function does not include this point. - **Behavior:** - This segment represents an increasing linear function from (-3, -2) to (0,1), excluding (-1,0). 2. **Second Segment:** - **Points:** - Starts from (1, 3) and includes the point (1,3) depicted by a hollow circle. - Ends at (3, -1) - **Line:** - The solid line connects the points (1, 3) and (3, -1). - **Behavior:** - This segment represents a decreasing linear function from (1, 3) to (3, -1). #### Interpretation - **Hollow Circles:** Indicate that the function is not defined at these particular points. - **Solid Dots:** Indicate that the function is defined at these points. ### Summary This piecewise function has two parts, separated at x-values -1 and 1, each representing a different linear behavior. The first segment increases from (-3, -2) to (0,1), excluding (-1,0), and the second segment decreases from (1, 3) to (3, -1), excluding (1,3). ### Educational Website Context This graph of a piecewise function is useful for demonstrating how functions can behave differently over different segments of their domain. Understanding piecewise functions is essential for grasping more complex functions and for solving real-world problems where functions may change behavior across different intervals.
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