Question
Describe the graph of the function f(x)=sin(23x)
as a transformation of its parent function.(1 point)
Responses
The graph is a horizontal compression by a factor of 23
.
The graph is a horizontal compression by a factor of Start Fraction 2 over 5 End Fraction .
The graph is a horizontal stretch by a factor of 23
.
The graph is a horizontal stretch by a factor of Start Fraction 5 over 2 End Fraction .
The graph is a vertical compression by a factor of 23
.
The graph is a vertical compression by a factor of Start Fraction 2 over 5 End Fraction .
The graph is a vertical stretch by a factor of 23
.
as a transformation of its parent function.(1 point)
Responses
The graph is a horizontal compression by a factor of 23
.
The graph is a horizontal compression by a factor of Start Fraction 2 over 5 End Fraction .
The graph is a horizontal stretch by a factor of 23
.
The graph is a horizontal stretch by a factor of Start Fraction 5 over 2 End Fraction .
The graph is a vertical compression by a factor of 23
.
The graph is a vertical compression by a factor of Start Fraction 2 over 5 End Fraction .
The graph is a vertical stretch by a factor of 23
.
Answers
GPT-4o mini
To analyze the function \( f(x) = \sin(23x) \) in relation to its parent function \( g(x) = \sin(x) \), we need to examine the effect of the coefficient 23 in front of \( x \).
The coefficient inside the sine function indicates a horizontal transformation:
- A coefficient greater than 1 (like 23) results in a **horizontal compression**.
- This compression factor is the reciprocal of the coefficient, thus it becomes \( \frac{1}{23} \).
Therefore, the graph of \( f(x) = \sin(23x) \) can be described as:
**The graph is a horizontal compression by a factor of \( \frac{1}{23} \)**.
However, since "by a factor of \( \frac{1}{23} \)" is not one of the options provided, we would select the closest statement regarding the transformation:
**The graph is a horizontal compression by a factor of 23**.
The coefficient inside the sine function indicates a horizontal transformation:
- A coefficient greater than 1 (like 23) results in a **horizontal compression**.
- This compression factor is the reciprocal of the coefficient, thus it becomes \( \frac{1}{23} \).
Therefore, the graph of \( f(x) = \sin(23x) \) can be described as:
**The graph is a horizontal compression by a factor of \( \frac{1}{23} \)**.
However, since "by a factor of \( \frac{1}{23} \)" is not one of the options provided, we would select the closest statement regarding the transformation:
**The graph is a horizontal compression by a factor of 23**.