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.
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