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Which of the following graphs is the correct plot of y = 3 cos(x)? 5t 5t -6 -5\-4 -3 -7 - 4 6 -5 -4 3 -2 -1 4 5 6 -6 -$ -4 -3 -2 -1 1/2 4 5 6 2 2 -3 -4 -4 -5 3 4/5 2. 2. 3. 2,

Which of the following graphs is the correct plot of y = 3 cos(x)? 5t 5t -6 -5\-4 -3 -7 - 4 6 -5 -4 3 -2 -1 4 5 6 -6 -$ -4 -3 -2 -1 1/2 4 5 6 2 2 -3 -4 -4 -5 3 4/5 2. 2. 3. 2,

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Title: Understanding the Graph of \( y = 3 \cos(x) \) **Question:** Which of the following graphs is the correct plot of \( y = 3 \cos(x) \)? Below, you'll find four different plots. Identify the correct graph that represents the function \( y = 3 \cos(x) \). The cosine function has an amplitude of 3, which means it oscillates between -3 and 3. **Options:** 1. **Graph 1:** - This graph oscillates between 5 and -5. - The points where it intersects the y-axis are at (0, 5), (-2π, -5), and (2π, -5). - The period appears to have been altered. 2. **Graph 2:** - This graph oscillates between 3 and -3. - The points where it intersects the y-axis are at (0, 3), (-2π, -3), and (2π, -3). - The period has not been altered from that of the standard cosine function, making the amplitude consistent with the function \( y = 3 \cos(x) \). 3. **Graph 3:** - This graph oscillates between 4 and -4. - The points where it intersects the y-axis are at (0, 4), (-2π, -4), and (2π, -4). - The period seems to have been altered, and so has the amplitude. 4. **Graph 4:** - This graph oscillates between 3 and -3. - The function appears to have the correct period and amplitude as well, but ensure to check intersections. **Correct Answer:** The proper plot for \( y = 3 \cos(x) \) must have its maximum and minimum values at 3 and -3, respectively, and the period should remain the same as the standard cosine function. Upon reviewing the provided graphs, **Graph 2** correctly represents the function \( y = 3 \cos(x) \) based on its amplitude and period. **Conclusion:** When identifying the graph of \( y = A \cos(x) \), always ensure that the graph’s amplitude is \( A \) and that there is no horizontal or vertical shift unless specified otherwise.
Transcribed Image Text:Title: Understanding the Graph of \( y = 3 \cos(x) \) **Question:** Which of the following graphs is the correct plot of \( y = 3 \cos(x) \)? Below, you'll find four different plots. Identify the correct graph that represents the function \( y = 3 \cos(x) \). The cosine function has an amplitude of 3, which means it oscillates between -3 and 3. **Options:** 1. **Graph 1:** - This graph oscillates between 5 and -5. - The points where it intersects the y-axis are at (0, 5), (-2π, -5), and (2π, -5). - The period appears to have been altered. 2. **Graph 2:** - This graph oscillates between 3 and -3. - The points where it intersects the y-axis are at (0, 3), (-2π, -3), and (2π, -3). - The period has not been altered from that of the standard cosine function, making the amplitude consistent with the function \( y = 3 \cos(x) \). 3. **Graph 3:** - This graph oscillates between 4 and -4. - The points where it intersects the y-axis are at (0, 4), (-2π, -4), and (2π, -4). - The period seems to have been altered, and so has the amplitude. 4. **Graph 4:** - This graph oscillates between 3 and -3. - The function appears to have the correct period and amplitude as well, but ensure to check intersections. **Correct Answer:** The proper plot for \( y = 3 \cos(x) \) must have its maximum and minimum values at 3 and -3, respectively, and the period should remain the same as the standard cosine function. Upon reviewing the provided graphs, **Graph 2** correctly represents the function \( y = 3 \cos(x) \) based on its amplitude and period. **Conclusion:** When identifying the graph of \( y = A \cos(x) \), always ensure that the graph’s amplitude is \( A \) and that there is no horizontal or vertical shift unless specified otherwise.
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