Answer: A
Step-by-step explanation:
To find the average rate of change, you use the formula [tex]\frac{f(b)-f(a)}{b-a}[/tex]. The best way to get the correct answer is to plug in each interval to make sure it equals 0.
-1 ≤ x ≤ 2: Correct
[tex]\frac{f(2)-f(-1)}{2-(-1)}[/tex] [solve for f(2) and f(1)]
[tex]\frac{1-1}{3}=\frac{0}{3} =0[/tex]
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-3 ≤ x ≤ -2: Incorrect
[tex]\frac{f(-2)-f(-3)}{-2-(-3)}[/tex] [solve for f(-2) and f(-3)]
[tex]\frac{5-11}{1} =\frac{-6}{1}=-6[/tex]
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-5 ≤ x ≤ 5: Incorrect
[tex]\frac{f(5)-f(-5)}{5-(-5)}[/tex] [solve for f(5) and f(-5)]
[tex]\frac{19-29}{10} =\frac{-10}{10} =-1[/tex]
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2 ≤ x ≤ 3: Incorrect
[tex]\frac{f(3)-f(2)}{3-2}[/tex] [solve for f(3) and f(2)]
[tex]\frac{5-1}{1} =\frac{4}{1} =4[/tex]
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After going through all the intervals, we found that A was the only one that has an average rate of change of 0.
