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For the graph below, give a restricted domain that includes x = 0 and the entire range of the function. 3 2 AA -pл-Sл-4-3-2- -2 w π2π 3 4π 5π όπ

For the graph below, give a restricted domain that includes x = 0 and the entire range of the function. 3 2 AA -pл-Sл-4-3-2- -2 w π2π 3 4π 5π όπ

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 the Restricted Domain of a Trigonometric Function** **Instructions:** For the graph below, provide a restricted domain that includes \( x = 0 \) and encompasses the entire range of the function. **Graph Description:** - The graph is sinusoidal and spans horizontally from \( -6\pi \) to \( 6\pi \). - The vertical axis ranges from -3 to 3. - The wave has peaks and troughs at regular intervals, indicating a periodic function. - The graph crosses the x-axis at integer multiples of \(\pi\), suggesting this is likely sine or cosine function. - Key points include: - Peaks at \( y = 3 \) - Troughs at \( y = -3 \) - Zero crossings at intervals of \(\pi\) **Task:** - Identify a portion of the graph that includes \( x = 0 \) and captures the complete range of function values, which are from -3 to 3. This graph represents a common trigonometric function, demonstrating the periodic nature of sine or cosine functions and the importance of selecting an appropriate domain to analyze their behavior effectively.
Transcribed Image Text:**Title: Understanding the Restricted Domain of a Trigonometric Function** **Instructions:** For the graph below, provide a restricted domain that includes \( x = 0 \) and encompasses the entire range of the function. **Graph Description:** - The graph is sinusoidal and spans horizontally from \( -6\pi \) to \( 6\pi \). - The vertical axis ranges from -3 to 3. - The wave has peaks and troughs at regular intervals, indicating a periodic function. - The graph crosses the x-axis at integer multiples of \(\pi\), suggesting this is likely sine or cosine function. - Key points include: - Peaks at \( y = 3 \) - Troughs at \( y = -3 \) - Zero crossings at intervals of \(\pi\) **Task:** - Identify a portion of the graph that includes \( x = 0 \) and captures the complete range of function values, which are from -3 to 3. This graph represents a common trigonometric function, demonstrating the periodic nature of sine or cosine functions and the importance of selecting an appropriate domain to analyze their behavior effectively.
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