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

"the addition of a negative constant"

Step-by-step 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.

the best buy, is the 4- kilogram bag of lollipops for $18.40.

step-by-step explanation:

i found my answer by dividing the cost of each bag by their respective weights.

14.88 divided by 2 = 7.44

17.29 divided by 3 = 5.77

18.4 divided by 4 = 4.6

24.4 divided by 5 = 4.88

by this, i found that the 4 kilo bag is the best buy.

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153