Final answer:
The function with the greatest rate of change on the interval from x= π to x=3 π/2 is function A.
Step-by-step explanation:
The rate of change is determined by the slope of the function. To compare the functions, we need to find the slopes or the derivatives. Let's calculate the derivatives of the functions and evaluate them at x = π and x = 3π/2.
A. f(x) = 3x - 2; f'(x) = 3
B. g(x) = -2x + 4; g'(x) = -2
C. h(x) = x - 3; h'(x) = 1
By evaluating the derivatives at the given x-values, we find that f'(x) = 3, g'(x) = -2, and h'(x) = 1. Therefore, function A has the greatest rate of change on the interval from x = π to x = 3π/2.