Final answer:
To determine the average rate of change of the quadratic function over an interval, calculate the difference in the function values at the endpoints and divide it by the difference in the x-values.
Step-by-step explanation:
To determine the average rate of change of the function f(x) = x² - 9x + 16 over the interval 1 ≤ x ≤ 9, we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values:
- Calculate f(9) - f(1): (9)² - 9(9) + 16 - (1)² - 9(1) + 16 = 64 - 81 = -17
- Calculate 9 - 1: 8
- Divide the result from step 1 by the result from step 2: -17/8 = -2.125
Therefore, the average rate of change of the function is -2.125.