The average rate of change over the given interval is
[tex]\dfrac{f(2) - f(-1)}{2 - (-1)} = \dfrac{f(2) - f(-1)}3[/tex]
According to the table, [tex]f(2) = 5[/tex], but [tex]f(-1)[/tex] is not given, so the best we can say is
[tex]\dfrac{f(2) - f(-1)}3= \dfrac{5 - f(-1)}3[/tex]
If you meant 1 instead of -1, then [tex]f(1) = 6[/tex], and the average rate of change would be
[tex]\dfrac{f(2) - f(1)}{2 - 1} = f(2) - f(1) = 5 - 6 = \boxed{-1}[/tex]
