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44 b L C N 1 N 3 2 N CH

44 b L C N 1 N 3 2 N CH

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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Solve correctly determine the domain and the range if the function
### Determine the Domain and Range of the Function The image shows a graph of a piecewise linear function. The function consists of two linear segments forming a "V" shape. Here's a detailed description of the graph: - **Axes and Labels**: The x-axis and y-axis are labeled, with increments marked at intervals of 1 unit. - **Line Segments**: - The left segment descends from the top left, starting at an unspecified higher point, passing through (-4, 4), (-3, 3), (-2, 2), (-1, 1), until it reaches the point (0, 0). - The right segment begins at (0, 0) and ascends to the right, passing through (1, 1), (2, 2), (3, 3), up towards an unspecified higher point. - **Direction Arrows**: Both ends of the lines have arrows, indicating that the function continues indefinitely in both directions. ### Domain and Range - **Domain**: The domain of this function is all real numbers. This is indicated by the arrows on both ends of the graph, showing that the function extends infinitely in both the negative and positive x-directions. - **Range**: The range of the function is all real numbers greater than or equal to zero \([0, \infty)\). This results from the lowest point of the graph being at y = 0, and the function values increasing as it extends vertically. This piecewise function is a classic example of an absolute value function, symmetric around the y-axis.
Transcribed Image Text:### Determine the Domain and Range of the Function The image shows a graph of a piecewise linear function. The function consists of two linear segments forming a "V" shape. Here's a detailed description of the graph: - **Axes and Labels**: The x-axis and y-axis are labeled, with increments marked at intervals of 1 unit. - **Line Segments**: - The left segment descends from the top left, starting at an unspecified higher point, passing through (-4, 4), (-3, 3), (-2, 2), (-1, 1), until it reaches the point (0, 0). - The right segment begins at (0, 0) and ascends to the right, passing through (1, 1), (2, 2), (3, 3), up towards an unspecified higher point. - **Direction Arrows**: Both ends of the lines have arrows, indicating that the function continues indefinitely in both directions. ### Domain and Range - **Domain**: The domain of this function is all real numbers. This is indicated by the arrows on both ends of the graph, showing that the function extends infinitely in both the negative and positive x-directions. - **Range**: The range of the function is all real numbers greater than or equal to zero \([0, \infty)\). This results from the lowest point of the graph being at y = 0, and the function values increasing as it extends vertically. This piecewise function is a classic example of an absolute value function, symmetric around the y-axis.
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