Option C: -3 is the average rate of change between [tex]x=-1[/tex] and [tex]x=1[/tex]
Explanation:
The formula to determine the average rate of change is given by
Average rate of change = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We need to find the average rate of change between [tex]x=-1[/tex] and [tex]x=1[/tex]
Thus, from the table, we have,
[tex]x_1=-1[/tex] , [tex]y_1=5[/tex]
[tex]x_2=1[/tex] , [tex]y_2=-1[/tex]
Thus, substituting these values in the formula, we get,
Average rate of change = [tex]\frac{-1-5}{1+1}[/tex]
[tex]=\frac{-6}{2}[/tex]
[tex]=-3[/tex]
Thus, the average rate of change between [tex]x=-1[/tex] and [tex]x=1[/tex] is -3.
Hence, Option C is the correct answer.
