Question

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

Are you sure

Answer 2

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 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!