Final answer:
The range of the function y = 2/3 sin x over the interval π ≤ x ≤ 2π is [-2/3, +2/3], as this represents the amplitude modification of a standard sine wave oscillating between -1 and 1.
Step-by-step explanation:
The range of y = ²/₃ sin x for π ≤ x ≤ 2π can be found by looking at the behavior of the sine function. The standard sine function, sin x, oscillates between +1 and -1. When you multiply this by ²/₃, the amplitude of the oscillation changes, but the range of the sine function remains between -²/₃ and +²/₃.
Since sin x reaches its maximum and minimum within one period, which is 2π, the given range of x values from π to 2π will cover a complete period of the sine wave. Therefore, the range of the function y = ²/₃ sin x over this interval is [-²/₃, +²/₃].