Answer: The average rate of change of a function on an interval can be found by calculating the slope of the line connecting the endpoints of the interval. In this case, the interval is -4 ≤ x ≤ -2.
To find the average rate of change, we need to determine the change in the function's values over the interval. We can do this by subtracting the y-values of the function at the endpoints of the interval. Let's call the y-values at x = -4 and x = -2 as y1 and y2, respectively.
Next, we calculate the change in the x-values by subtracting the endpoints of the interval. In this case, the change in x is -2 - (-4) = 2.
Finally, we can calculate the average rate of change by dividing the change in y-values by the change in x-values:
Average rate of change = (y2 - y1) / (x2 - x1)
Substituting the values we found earlier:
Average rate of change = (y2 - y1) / 2
Now, look at the graph and determine the y-values at x = -4 and x = -2. Once you have those values, subtract y1 from y2 and divide the result by 2 to find the average rate of change of the function on the interval -4 ≤ x ≤ -2.
Please let me know if you have any specific values for y1 and y2, so I can help you calculate the average rate of change.