On a sine function y = Asin (Bx) + C, the maximum value is 19 and the minimum value is - 5. Which of the following must be the value of |A| - C?

|A| - C = 5

Step-by-step explanation:

The maximum value that a sine function can have is 1, and the minimum value is - 1.

With this information, to find the minimum value of y, we can use sin (Bx) = - 1, and to find the maximum value, we can use sin (Bx) = 1. Then, we have that:

19 = A + C

-5 = - A + C

Summing both equations, we have:

14 = 2C

C = 7

Now, to find the value of A, we can use the first equation:

19 = A + C

19 = A + 7

A = 12

So the value of |A| - C is:

|12| - 7 = 12 - 7 = 5