**Question** Determine the magnitude and direction of the vertical shift and the phase shift for the function below. \[ f(x) = \sin \left( x + \frac{\pi}{3} \right) - 4 \] Select the correct answer below: - ☐ The vertical shift is \(\frac{\pi}{3}\) units down, and the phase shift is 4 units left. - ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units left. - ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units right. - ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units left. - ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units right. - ☐ The vertical shift is \(\frac{\pi}{3}\) units up, and the phase shift is 4 units right.
**Question** Determine the magnitude and direction of the vertical shift and the phase shift for the function below. \[ f(x) = \sin \left( x + \frac{\pi}{3} \right) - 4 \] Select the correct answer below: - ☐ The vertical shift is \(\frac{\pi}{3}\) units down, and the phase shift is 4 units left. - ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units left. - ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units right. - ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units left. - ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units right. - ☐ The vertical shift is \(\frac{\pi}{3}\) units up, and the phase shift is 4 units right.
Trigonometry (11th Edition)
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°.
Related questions
Question
![**Question**
Determine the magnitude and direction of the vertical shift and the phase shift for the function below.
\[ f(x) = \sin \left( x + \frac{\pi}{3} \right) - 4 \]
Select the correct answer below:
- ☐ The vertical shift is \(\frac{\pi}{3}\) units down, and the phase shift is 4 units left.
- ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units left.
- ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units right.
- ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units left.
- ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units right.
- ☐ The vertical shift is \(\frac{\pi}{3}\) units up, and the phase shift is 4 units right.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F210ef24a-00e7-4179-8f1e-410e45889c5f%2Fe5fab03f-c357-47f4-9a09-0d68dd820c98%2Fk4l51u.jpeg&w=3840&q=75)
Transcribed Image Text:**Question**
Determine the magnitude and direction of the vertical shift and the phase shift for the function below.
\[ f(x) = \sin \left( x + \frac{\pi}{3} \right) - 4 \]
Select the correct answer below:
- ☐ The vertical shift is \(\frac{\pi}{3}\) units down, and the phase shift is 4 units left.
- ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units left.
- ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units right.
- ☐ The vertical shift is 4 units up, and the phase shift is \(\frac{\pi}{3}\) units left.
- ☐ The vertical shift is 4 units down, and the phase shift is \(\frac{\pi}{3}\) units right.
- ☐ The vertical shift is \(\frac{\pi}{3}\) units up, and the phase shift is 4 units right.
Expert Solution
Step 1
Given function is .
We know that if we have function then there is phase shift of to the right of function .
Therefore, from the given function, we can say that phase shift is to the right.
We know that if k is a positive number then the graph of is the graph of shifted downwards k units.
Therefore, the graph of given function will be shifted downwards by 4 units.
Hence, correct answer is "The vertical shift is 4 units down and the phase shift is units right.
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