Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
The image presents a series of six graphs labeled A through F. Each graph depicts a sine or cosine wave function with varying frequency and amplitude. Below each graph is the expression "y =" followed by an empty box, presumably for identifying or matching the equations of the graphs. **Graph Analysis:** - **Graph A:** Displays a sine wave with a single cycle over the interval from 0 to 2π, indicating a standard sine function with an amplitude of 1. - **Graph B:** Similar to Graph A, Graph B features a sine wave starting at 0 and completing a single cycle by 2π, also suggesting a typical sine function. - **Graph C:** Shows a sine wave with a higher frequency, completing multiple oscillations between 0 and 2π, inferring a higher frequency sine function than A or B. - **Graph D:** Similar to Graph C, Graph D illustrates multiple oscillations, suggesting another high-frequency sine function but possibly with a different amplitude or phase shift. - **Graph E:** Similar to Graphs C and D, Graph E portrays multiple cycles within 0 to 2π, indicating a high-frequency sine wave with possible alterations in amplitude or phase. - **Graph F:** Exhibits sine wave characteristics with a lower frequency compared to graphs C, D, and E but higher than A and B, possibly including phase shifts or amplitude changes. Each graph provides visual data for understanding the effects of changing frequency and amplitude on sine waves. The intention is likely for users to match the graphs with relevant trigonometric functions.
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Transcribed Image Text:The image presents a series of six graphs labeled A through F. Each graph depicts a sine or cosine wave function with varying frequency and amplitude. Below each graph is the expression "y =" followed by an empty box, presumably for identifying or matching the equations of the graphs. **Graph Analysis:** - **Graph A:** Displays a sine wave with a single cycle over the interval from 0 to 2π, indicating a standard sine function with an amplitude of 1. - **Graph B:** Similar to Graph A, Graph B features a sine wave starting at 0 and completing a single cycle by 2π, also suggesting a typical sine function. - **Graph C:** Shows a sine wave with a higher frequency, completing multiple oscillations between 0 and 2π, inferring a higher frequency sine function than A or B. - **Graph D:** Similar to Graph C, Graph D illustrates multiple oscillations, suggesting another high-frequency sine function but possibly with a different amplitude or phase shift. - **Graph E:** Similar to Graphs C and D, Graph E portrays multiple cycles within 0 to 2π, indicating a high-frequency sine wave with possible alterations in amplitude or phase. - **Graph F:** Exhibits sine wave characteristics with a lower frequency compared to graphs C, D, and E but higher than A and B, possibly including phase shifts or amplitude changes. Each graph provides visual data for understanding the effects of changing frequency and amplitude on sine waves. The intention is likely for users to match the graphs with relevant trigonometric functions.
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