Final answer:
The average rate of change of the function f(x) = 5x + 8 over the interval [-19, -9] is 5, calculated by taking the difference in function values at the endpoints of the interval and dividing by the length of the interval.
Step-by-step explanation:
The student is asking to find the average rate of change of the function f(x) = 5x + 8 over the interval [ -19, -9]. This can be done by calculating the difference in the y-values of the function at the endpoints of the interval and dividing this by the difference in the x-values of the interval (∆y/∆x).
Firstly, find the function values at x = -19 and x = -9:
- f(-19) = 5(-19) + 8 = -95 + 8 = -87
- f(-9) = 5(-9) + 8 = -45 + 8 = -37
Next, calculate the changes:
- Change in y (∆y) = f(-9) - f(-19) = -37 - (-87) = 50
- Change in x (∆x) = -9 - (-19) = 10
Finally, the average rate of change is:
Average rate of change = ∆y / ∆x = 50 / 10 = 5
The average rate of change of the function f(x) = 5x + 8 over the interval [ -19, -9] is 5.