Final answer:
Function A, g(x) = x^2 + 4x - 8, has a greater average rate of change over the interval [1, 2] since its average rate of change is 7, while function B's average rate of change is zero.
Step-by-step explanation:
To compare the average rate of change of functions A and B over the interval [1, 2], we calculate the average rate for each function using the formula:
Average Rate of Change = ∆y / ∆x = (f(2) - f(1)) / (2 - 1)
For Function A, g(x) = x^2 + 4x - 8:
g(2) = 2^2 + 4(2) - 8 = 4
g(1) = 1^2 + 4(1) - 8 = -3
So the average rate of change for A is (4 - (-3)) / (2 - 1) = 7.
For Function B, h(x) = x^2 - 3x + 6:
h(2) = 2^2 - 3(2) + 6 = 4
h(1) = 1^2 - 3(1) + 6 = 4
Therefore, the average rate of change for B is (4 - 4) / (2 - 1) = 0.
The function A has a greater average rate of change over the interval [1, 2] compared to function B, which has an average rate of change of zero.