Final answer:
To determine which function has a greater average rate of change over the given interval, we calculate the average rate of change for both functions and compare them. The function g(x) = -4x - 8 has a greater average rate of change than the function f(x) = x² + 5x + 4 over the interval -3 ≤ x ≤ 2.
Step-by-step explanation:
To determine which function has the greater average rate of change over the interval -3 ≤ x ≤ 2, we need to calculate the average rate of change for both functions. The average rate of change of a function over an interval is found by taking the difference in the function values at the endpoints of the interval and dividing it by the difference in the x-values.
For f(x) = x² + 5x + 4, we have f(-3) = (-3)² + 5(-3) + 4 = 22 and f(2) = (2)² + 5(2) + 4 = 22. So, the average rate of change for f(x) is (22 - 22)/(-3 - 2) = 0.
For g(x) = -4x - 8, we have g(-3) = -4(-3) - 8 = 4 and g(2) = -4(2) - 8 = -16. So, the average rate of change for g(x) is (-16 - 4)/(2 - (-3)) = -20/5 = -4.
Therefore, the function g(x) = -4x - 8 has a greater average rate of change over the interval -3 ≤ x ≤ 2.