Final answer:
The range of the function f(x) = -3sin(3x) + 8 is from 5 to 11.
Step-by-step explanation:
The function f(x) = -3sin(3x) + 8 is a transformation of the basic sine wave. The sine function has a range of -1 to 1, and by multiplying this by -3, we stretch the amplitude to 3 but also invert it due to the negative sign. The addition of 8 then shifts the entire function upwards by 8 units. Therefore, the maximum value of the function occurs when sin(3x) = -1, which would be -3(-1) + 8 = 11 and the minimum value when sin(3x) = 1, which would be -3(1) + 8 = 5. So, the range of the function is [5, 11].