Answer:
A. -19
Step-by-step explanation:
There are lots of ways to get there. One of them is to realize that the average rate of change between two adjacent numbers is the negative of their sum. -(9+10) = -19.
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Another is to extend the table:
6 to 7 : -13
7 to 8 : -15
8 10 9 : -17
9 to 10 : -19
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Yet another is to write an equation for the function, and compute the average rate of change:
f(x) = -x^2 -1
average rate of change from 9 to 10 = (f(10) -f(9))/(10 -9) = (-101 -(-82))/(10 -9) = -19
