The average rate of change over the interval [-9, -3] is
[tex]\dfrac{f(-3) - f(-9)}{-3 - (-9)}[/tex]
That is, it's the ratio between the change in the function value over the length of the interval. Judging by the plot, we have f (-9) = 6 and f (-3) = -3. So the average rate of change is
[tex]\dfrac{f(-3) - f(-9)}{-3 - (-9)} = \dfrac{-3 - 6}{-3 + 9} = -\dfrac96 = \boxed{-\dfrac32}[/tex]
