Final answer:
The vertical translation of a transformed sine function with a maximum value of 8 and a minimum value of -2 is 3, calculated as the average of the maximum and minimum values.
Step-by-step explanation:
The vertical translation of a sine function can be determined by finding the average of the maximum and minimum values of the function. A sine function normally oscillates between +1 and -1, but when it is transformed, its maximum and minimum points change.
In this case, the maximum value of the transformed sine function is 8 and the minimum value is -2. To find the vertical translation, you calculate the average of these two values. This can be done by using the formula:
Vertical Translation = (Maximum value + Minimum value) / 2
Plugging in the values, we get:
Vertical Translation = (8 + (-2)) / 2
Vertical Translation = 6 / 2
Vertical Translation = 3
Therefore, the vertical translation of the transformed sine function is 3 units.