Use the formula f(b)-f(a)/b-a to calculate the average rate of change over the interval [-2,0] given the function table for f(x)=x^2+6x+8. Express your answer as an integer.
x / f(x)
-3 / -1
-2 / 0
-1 / 3
0 / 8
The average rate of change is ___.
To calculate the average rate of change over the interval [-2,0] for the function $ f(x) = x^2 + 6x + 8 $, we need to use the formula:
$ \frac{f(b) - f(a)}{b - a} $
where $ a = -2 $ and $ b = 0 $.
Using the function table provided:
$ f(-2) = 0 $
$ f(0) = 8 $
Therefore:
$ \frac{f(0) - f(-2)}{0 - (-2)} = \frac{8 - 0}{2} = \frac{8}{2} = 4 $
The average rate of change over the interval [-2,0] for the function $ f(x) = x^2 + 6x + 8 $ is 4.
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(0-0)/(-2-(-3)) = 0 / 1 = 0
Therefore, the average rate of change over the interval [-2,0] for f(x) = x^2 + 6x + 8 is 0.