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Determine the intervals on which the function is increasing, decreasing, and constant.

Determine the intervals on which the function is increasing, decreasing, and constant.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Title: Understanding Function Behavior** **Determine the intervals on which the function is increasing, decreasing, and constant.** **Graph Description:** In the given graph, we observe a function plotted over the x-y coordinate plane. The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5. The function consists of several distinct segments: 1. **Constant Segment:** - From x = -5 to x = -3, the function is constant at y = 2. 2. **Increasing Segment:** - From x = -2 to x = 0, the function increases from y = -3 to y = 3. 3. **Decreasing Segment:** - From x = 1 to x = 3, the function decreases from y = 3 to y = 1. 4. **Increasing Segment:** - From x = 3 to x = 5, the function increases from y = 0 to y = 3. **Options for Behavior Analysis:** - A) Increasing on (-2, 0) and (3, 4); Decreasing on (-5, -2) and (1, 3) - B) Increasing on (1, 3); Decreasing on (-2, 0) and (3, 5); Constant on (2, 5) - C) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -3) - D) Increasing on (-1, 0) and (3, 5); Decreasing on (0, 3); Constant on (-5, -3) **Correct Analysis:** - The function is constant on (-5, -3). - It is increasing on (-2, 0) and (3, 5). - It is decreasing on (1, 3). Thus, the correct option that fits the graph's behavior is: **C) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -3).**
Transcribed Image Text:**Title: Understanding Function Behavior** **Determine the intervals on which the function is increasing, decreasing, and constant.** **Graph Description:** In the given graph, we observe a function plotted over the x-y coordinate plane. The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5. The function consists of several distinct segments: 1. **Constant Segment:** - From x = -5 to x = -3, the function is constant at y = 2. 2. **Increasing Segment:** - From x = -2 to x = 0, the function increases from y = -3 to y = 3. 3. **Decreasing Segment:** - From x = 1 to x = 3, the function decreases from y = 3 to y = 1. 4. **Increasing Segment:** - From x = 3 to x = 5, the function increases from y = 0 to y = 3. **Options for Behavior Analysis:** - A) Increasing on (-2, 0) and (3, 4); Decreasing on (-5, -2) and (1, 3) - B) Increasing on (1, 3); Decreasing on (-2, 0) and (3, 5); Constant on (2, 5) - C) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -3) - D) Increasing on (-1, 0) and (3, 5); Decreasing on (0, 3); Constant on (-5, -3) **Correct Analysis:** - The function is constant on (-5, -3). - It is increasing on (-2, 0) and (3, 5). - It is decreasing on (1, 3). Thus, the correct option that fits the graph's behavior is: **C) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -3).**
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