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f(x) = 2 sin(x) +x %3D -5 (-Απ/3,-2.457). (-2т/3, —3.826)

f(x) = 2 sin(x) +x %3D -5 (-Απ/3,-2.457). (-2т/3, —3.826)

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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I have tried -2pi/3,-4pi/3 and the computer does not accept. Not sure what I’m doing wrong
**Using the Graphing Utility to Graph \( f(x) = 2 \sin(x) + x \)** This image displays a graph created with Desmos, an online graphing utility, to visualize the function \( f(x) = 2 \sin(x) + x \). ### Graph Explanation - **Function**: The graph represents \( f(x) = 2 \sin(x) + x \). - **Axes**: The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \). - **Graph Features**: - The curve demonstrates an oscillating sine function with an additional linear component \( x \), causing a phase shift and change in amplitude compared to the standard sine wave. - There are two labeled points on the graph: - \( (-\frac{4\pi}{3}, -2.457) \) - \( (-\frac{2\pi}{3}, -3.826) \) The graph visually illustrates how the linear term \( x \) affects the sine wave, resulting in a transformed wave pattern. The labeled points help pinpoint specific coordinates for analysis.
Transcribed Image Text:**Using the Graphing Utility to Graph \( f(x) = 2 \sin(x) + x \)** This image displays a graph created with Desmos, an online graphing utility, to visualize the function \( f(x) = 2 \sin(x) + x \). ### Graph Explanation - **Function**: The graph represents \( f(x) = 2 \sin(x) + x \). - **Axes**: The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \). - **Graph Features**: - The curve demonstrates an oscillating sine function with an additional linear component \( x \), causing a phase shift and change in amplitude compared to the standard sine wave. - There are two labeled points on the graph: - \( (-\frac{4\pi}{3}, -2.457) \) - \( (-\frac{2\pi}{3}, -3.826) \) The graph visually illustrates how the linear term \( x \) affects the sine wave, resulting in a transformed wave pattern. The labeled points help pinpoint specific coordinates for analysis.
**Transcription for Educational Website** --- **Graph Description:** The graph displayed on the left depicts a section of a trigonometric function, likely sinusoidal, with a focus on the interval \([-2\pi, 0]\). The x-axis represents the interval in question, with important intercepts at approximately \(-2\pi\) and 0. The y-axis shows vertical values ranging from around -10 to 5, suggesting significant oscillation within this range. **Instruction:** Identify the locations of transition points on the interval \([-2\pi, 0]\). (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use \(\pi\) where needed.) **Student Response:** \( f \) has transition points at \( x = \frac{4\pi}{3}, \frac{2\pi}{3}, 0 \). **Feedback:** Incorrect --- This transcription serves as an educational guide for identifying transition points in trigonometric graphs, aiding students in understanding the critical points on specified intervals.
Transcribed Image Text:**Transcription for Educational Website** --- **Graph Description:** The graph displayed on the left depicts a section of a trigonometric function, likely sinusoidal, with a focus on the interval \([-2\pi, 0]\). The x-axis represents the interval in question, with important intercepts at approximately \(-2\pi\) and 0. The y-axis shows vertical values ranging from around -10 to 5, suggesting significant oscillation within this range. **Instruction:** Identify the locations of transition points on the interval \([-2\pi, 0]\). (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use \(\pi\) where needed.) **Student Response:** \( f \) has transition points at \( x = \frac{4\pi}{3}, \frac{2\pi}{3}, 0 \). **Feedback:** Incorrect --- This transcription serves as an educational guide for identifying transition points in trigonometric graphs, aiding students in understanding the critical points on specified intervals.
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