Which of the following accurately describes a transformation to the parent function that results in y=−3.6cosx ?(1 point) Responses The amplitude of the parent function was changed from 0 to 3.6. The amplitude of the parent function was changed from 0 to 3.6. The graph of the parent function is reflected across the x-axis. The graph of the parent function is reflected across the x -axis. The graph of the parent function is vertically compressed by 3.6. The graph of the parent function is vertically compressed by 3.6. The graph of the parent function is vertically translated down 3.6 units.

Question

GPT-4o mini · Answer

To analyze the transformation resulting in \( y = -3.6 \cos x \):

Amplitude: The amplitude of a cosine function \( y = a \cos x \) is given by the absolute value of \( a \). In this case, \( a = -3.6 \), so the amplitude is \( | -3.6 | = 3.6 \). Thus, it can be said that the amplitude changed from 1 (the amplitude of the parent function \( y = \cos x \)) to 3.6. However, it's more accurate to say that the amplitude itself changed to 3.6, not from 0 to 3.6.
Reflection: Since \( a \) is negative (\( -3.6 \)), this means that the graph of the cosine function is reflected across the x-axis.
Vertical Compression: The term "vertically compressed" usually refers to a situation where the amplitude is between 0 and 1. Here, the graph is actually stretched by a factor of 3.6 and then reflected across the x-axis.
Vertical Translation: There is no vertical translation in \( y = -3.6 \cos x \) since there is no added or subtracted constant outside the function.

Based on these points, the correct choice from the options provided is:

The graph of the parent function is reflected across the x-axis.