To analyze the transformation from the parent function \( y = \cos x \) to \( y = -3.6 \cos x \), let's break it down:
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Amplitude: The amplitude of the cosine function is the coefficient in front of the cosine function. In this case, the amplitude is given by the absolute value of \(-3.6\), which is \(3.6\). So, the amplitude was changed from \(1\) (the original amplitude of the cosine function) to \(3.6\).
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Reflection: The negative sign in front of the \(3.6\) indicates that the graph has been reflected across the x-axis. This means that the peaks of the cosine function will become troughs and vice versa.
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Vertical Compression: The term "vertically compressed" typically refers to multiplying the function by a factor less than 1. Since \(-3.6\) is greater than 1 in absolute value, it does not indicate a compression; instead, it indicates a change in amplitude along with the reflection.
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Vertical Translation: There is no vertical translation in this transformation because there is no addition or subtraction outside the cosine function.
Given these points, the most accurate description of the transformation to the parent function \( y = \cos x \) that results in \( y = -3.6 \cos x \) is:
The graph of the parent function is reflected across the x-axis.
This is the correct answer among the provided options.
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