**Question 7**: Identify the correct graph of the function \( y = -3 \sin \left(\frac{1}{3}x\right) \).**Graphs Description:****A)** The graph displays a sine wave that oscillates between 3 and -3 on the y-axis. It completes two full cycles between \(-2\pi\) and \(2\pi\) on the x-axis. The wave begins at the origin and first moves downward, indicating a reflection over the x-axis.**B)** This graph shows a single cycle of a sine wave between \(-2\pi\) and \(2\pi\) on the x-axis. It peaks above the x-axis and valleys below.**C)** The graph depicts a sine wave that has a smooth curve, starting at the origin and curving downward, but completing much less than a full cycle between \(-2\pi\) and \(2\pi\).**D)** This graph shows a sine wave similar to option A. However, the wave completes two full cycles between \(-2\pi\) and \(2\pi) and starts by moving downward, indicating a similar reflection over the x-axis.**Explanation:**The function \( y = -3 \sin \left(\frac{1}{3}x\right) \) indicates an amplitude of 3 and a vertical reflection over the x-axis due to the negative sign. The period of the sine function is expanded to \(6\pi\) due to the \(\frac{1}{3}\) coefficient.**Correct Graph:** The answer is option **D**, as it correctly reflects the amplitude, the vertical reflection, and the periodicity of the given sine function.

Answered: 7) y = -3 sin x A) B) -21 -21 21 D) -2n…

7) y = -3 sin x A) B) -21 -21 21 D) -2n - 2n -2n

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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