Question

Which of the following accurately describes a transformation to the parent function that results in y=−3.6cos x ?(1 point) Responses The graph of the parent function is vertically translated down 3.6 units. The graph of the parent function is vertically translated down 3.6 units. 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 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 vertically compressed by 3.6. The graph of the parent function is vertically compressed by 3.6.

Answer 1

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

In the function \(y = -3.6 \cos x\):

1. The negative sign indicates that the graph is reflected across the x-axis.
2. The amplitude is 3.6 (not changed from 0), which describes the maximum height of the wave.
3. The function does not translate vertically; it reflects and scales vertically instead.

So the reflection across the x-axis is the key transformation applied to the parent cosine function.