Which of the following accurately describes a transformation to the parent function that results in y = -3.6 \cos x?

Question

A. The graph of the parent function is vertically compressed by 3.6.
B. The graph of the parent function is reflected across the x-axis.
C. The amplitude of the parent function was changed from 0 to 3.6.
D. The graph of the parent function is vertically translated down 3.6 units.

Answer 1

To analyze the transformation to the parent function \( y = \cos x \) that results in \( y = -3.6 \cos x \), we can examine each option:

1. A. The graph of the parent function is vertically compressed by 3.6.

   • This statement is incorrect. A vertical compression would mean that the amplitude is less than 1. In this case, the amplitude is 3.6.

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

   • This statement is correct. The negative sign in front of the cosine function indicates that the graph is reflected across the x-axis.

3. C. The amplitude of the parent function was changed from 0 to 3.6.

   • This statement is incorrect. The amplitude of the cosine function is not changing from 0; it changes from 1 (the amplitude of the parent function) to 3.6. The amplitude is actually the absolute value of the coefficient in front of the cosine, which is 3.6 here.

4. D. The graph of the parent function is vertically translated down 3.6 units.

   • This statement is incorrect. There is no vertical translation in this transformation. The negative sign reflects the graph, but it does not translate it down; the entire graph is simply flipped over the x-axis.

Thus, the correct answer is:

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

Answer 2

Are you sure

Answer 3

Yes, let's clarify the transformations specifically involved in changing the parent function \( y = \cos(x) \) to \( y = -3.6 \cos(x) \).

• The parent function \( y = \cos(x) \) has an amplitude of 1.
• The function \( y = -3.6 \cos(x) \) has an amplitude of 3.6 (the absolute value of the coefficient), but the negative sign indicates that it is reflected across the x-axis.

Now, breaking down the options again:

1. A. The graph of the parent function is vertically compressed by 3.6.

   • This is incorrect. A vertical compression means reducing the amplitude, but here the amplitude has increased to 3.6.

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

   • This is correct. The negative sign indicates that the graph of the cosine function is reflected across the x-axis.

3. C. The amplitude of the parent function was changed from 0 to 3.6.

   • This is incorrect. The amplitude goes from 1 (parent function) to 3.6, not 0.

4. D. The graph of the parent function is vertically translated down 3.6 units.

   • This is incorrect. There is no vertical translation; the graph is flipped due to the negative sign.

So, the answer confirming the transformation remains B: The graph of the parent function is reflected across the x-axis. If you have any doubts or further questions, feel free to ask!