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)=x2+6x+8. Express your answer as an integer.
To calculate the average rate of change over the interval [−2,0], we need to find the values of f(a) and f(b) using the function table provided for f(x) = x^2 + 6x + 8.
For a = -2:
f(a) = (-2)^2 + 6*(-2) + 8
= 4 - 12 + 8
= 0
For b = 0:
f(b) = (0)^2 + 6*(0) + 8
= 0 + 0 + 8
= 8
Now, using the formula f(b)−f(a)/b−a, we get:
(8 - 0) / (0 - (-2))
= 8 / 2
= 4
Therefore, the average rate of change over the interval [−2,0] is 4.