Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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I need to know if it’s A B C D OR E
![The problem presented is:
**"What is the phase shift of the following function?"**
\( f(x) = 2 \sin(3x + 6) - 1 \)
With the following multiple-choice options:
- ○ -1
- ○ 3
- ○ 2
- ○ -2
- ○ -6
To calculate the phase shift of the given trigonometric function, we need to examine the argument of the sine function, \(3x + 6\).
The general form of a sine function with a phase shift is given by:
\[ y = a \sin(bx + c) + d \]
In this form:
- \( a \) is the amplitude.
- \( b \) is the frequency.
- \( c \) is the phase shift (horizontal shift).
- \( d \) is the vertical shift.
The phase shift \( \phi \) is calculated using the formula:
\[ \phi = -\frac{c}{b} \]
For our function \( f(x) = 2 \sin(3x + 6) - 1 \):
- \( b = 3 \)
- \( c = 6 \)
Applying the formula for phase shift:
\[ \phi = -\frac{6}{3} = -2 \]
Therefore, the correct answer is:
- ○ -2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e4ee6c-a715-4803-9fbe-92a41a442b45%2F091b927a-5b0c-49dd-89a1-cd0622c38807%2Fnp05c1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented is:
**"What is the phase shift of the following function?"**
\( f(x) = 2 \sin(3x + 6) - 1 \)
With the following multiple-choice options:
- ○ -1
- ○ 3
- ○ 2
- ○ -2
- ○ -6
To calculate the phase shift of the given trigonometric function, we need to examine the argument of the sine function, \(3x + 6\).
The general form of a sine function with a phase shift is given by:
\[ y = a \sin(bx + c) + d \]
In this form:
- \( a \) is the amplitude.
- \( b \) is the frequency.
- \( c \) is the phase shift (horizontal shift).
- \( d \) is the vertical shift.
The phase shift \( \phi \) is calculated using the formula:
\[ \phi = -\frac{c}{b} \]
For our function \( f(x) = 2 \sin(3x + 6) - 1 \):
- \( b = 3 \)
- \( c = 6 \)
Applying the formula for phase shift:
\[ \phi = -\frac{6}{3} = -2 \]
Therefore, the correct answer is:
- ○ -2
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