By definition we have that the average rate of change of the function is:

Evaluating the function for the complete interval we have that the AVR is given by:

Rewriting we have:

Simplifying the expression we have:


Answer:
the average rate of change of the function defined by the table is:

4 in (4,-5) implies positive x-axis.
-5 in (4,-5) implies negative y-axis.
Since x is positive and y is negative in fourth quadrant, so the answer is
QUADRANT IV (or 4th quadrant.