Hat is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]? x f(x) -6 2.5 -2 2.5 0 2 2 0 3 5 5 2.5 1 0.5

Your table of values is so difficult to read that many of us helpers would just skip your post.

xf(x) -62.5 -2 2.5 02 20 35 5 2.5 1 0.5  could be put into far clearer format as follows:

 x   f(x)
--  
-6  2.5
-2  2.5
and so on.  Please fix it.

The "average rate of change" formula is 

                  f(x2) - f(x1)
av r of c =
                     x2-x1

so if you go from (-6, 2.5) to (2.5, 10.5), the av r of c would be
                  
                 10.5 - 2.5            9        18
              = =
                 2.5-(-6)            8.5         17

This may or may not be your final answer.  Again, please put your data table into readable form and then find the av r of c over the interval [-2,3].