In every case, the first given x is smaller than the second given x (e. g., in A, x=0 is smaller than x=6. Thus, the change in x from 0 to 6 is positive.
A: Evaluate f(0) and f(6): results are 0 and -9. We see that the change in the function value from x=0 to x=6 is negative, so A is not an answer.
B: Evaluate f(6) and f(8): We get -9 and 0. This is a positive change, so B could be an answer to this question.
C. We already have f(0) and f(8); they are 0 and 0. Thus, there is no net change in the function as we progress from x=0 to x=8. C is not an answer.
D. f(0) = 0, and f(2) = -3. Here the function decreases, so D is not an answer.
the function has a positive average rate of change from x=6 to x=8, and so the correct answer to this question is B.
