G(x)=− 4 x 2 +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, start superscript, 2, end superscript, divided by, 4, end fraction, plus, 7 what is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?

For this case, what we should do is evaluate the function for different points within the range shown.
 We then have the following table:
 x      g(x) 
 -2    -9
 -1     3
  0    7
  1    3
  2   -9
  3    -29
  4    -57
 From where we observed that the average rate of change is:
 -13
 
 the average rate of change of g over the interval [-2,4] is:
 -13