Question
Identify and interpret the amplitude of the function f left parenthesis t right parenthesis equals 3 sine left parenthesis 5 t minus Start Fraction pi over 8 End Fraction plus 7.
(1 point)
Responses
The amplitude is 3, and the graph is vertically stretched by a factor of 3.
The amplitude is 3, and the graph is vertically stretched by a factor of 3.
The amplitude is 3, and the graph is vertically compressed by a factor of 3.
The amplitude is 3, and the graph is vertically compressed by a factor of 3.
The amplitude is Start Fraction 2 pi over 3 End Fraction, and the graph is vertically stretched by a factor of Start Fraction 2 pi over 3 End Fraction.
The amplitude is Image with alt text: Start Fraction 2 pi over 3 End Fraction , and the graph is vertically stretched by a factor of Image with alt text: Start Fraction 2 pi over 3 End Fraction .
The amplitude is Start Fraction 2 pi over 3 End Fraction, and the graph is vertically compressed by a factor of Start Fraction 2 pi over 3 End Fraction.
(1 point)
Responses
The amplitude is 3, and the graph is vertically stretched by a factor of 3.
The amplitude is 3, and the graph is vertically stretched by a factor of 3.
The amplitude is 3, and the graph is vertically compressed by a factor of 3.
The amplitude is 3, and the graph is vertically compressed by a factor of 3.
The amplitude is Start Fraction 2 pi over 3 End Fraction, and the graph is vertically stretched by a factor of Start Fraction 2 pi over 3 End Fraction.
The amplitude is Image with alt text: Start Fraction 2 pi over 3 End Fraction , and the graph is vertically stretched by a factor of Image with alt text: Start Fraction 2 pi over 3 End Fraction .
The amplitude is Start Fraction 2 pi over 3 End Fraction, and the graph is vertically compressed by a factor of Start Fraction 2 pi over 3 End Fraction.
Answers
GPT-4o mini
The amplitude of a sine function in the form \( f(t) = A \sin(Bt - C) + D \) is given by the absolute value of the coefficient \( A \).
In the function \( f(t) = 3 \sin(5t - \frac{\pi}{8}) + 7 \), the coefficient \( A \) is 3.
Thus, the amplitude is 3, meaning the maximum value of the function will be 3 units above the midline, and the minimum value will be 3 units below the midline.
Therefore, we can conclude:
- The amplitude is 3, and the graph is vertically stretched by a factor of 3.
So the correct response is:
**The amplitude is 3, and the graph is vertically stretched by a factor of 3.**
In the function \( f(t) = 3 \sin(5t - \frac{\pi}{8}) + 7 \), the coefficient \( A \) is 3.
Thus, the amplitude is 3, meaning the maximum value of the function will be 3 units above the midline, and the minimum value will be 3 units below the midline.
Therefore, we can conclude:
- The amplitude is 3, and the graph is vertically stretched by a factor of 3.
So the correct response is:
**The amplitude is 3, and the graph is vertically stretched by a factor of 3.**