Question

The graphs of two cosine functions are shown below.

The function whose graph is B was obtained from the function whose graph is A by one of the following changes. That change was:

the addition of a negative constant

a change in amplitude

a phase shift

a period change

Answer 1

"the addition of a negative constant"

Explanation:

Please note the following points of functions regarding transformations:

1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant

2. If there is a phase shift, the function would be horizontally transformed

3. If there is a period change, the function would be horizontally compressed/stretched

4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.

We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.