Question

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
.

x f(x)
-3 -1
-2 0
-1 3
0 8


(1 point)

Answer 1

To calculate the average rate of change of the function \( f(x) = x^2 + 6x + 8 \) over the interval \([-2, 0]\), we will apply the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

Here, \( a = -2 \) and \( b = 0 \).

1. We need to find \( f(-2) \) and \( f(0) \):

From the provided function table:
- \( f(-2) = 0 \)
- \( f(0) = 8 \)

2. Now we can substitute these values into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{f(0) - f(-2)}{0 - (-2)} = \frac{8 - 0}{0 + 2} = \frac{8}{2} = 4
\]

Thus, the average rate of change of the function \( f(x) \) over the interval \([-2, 0]\) is \(\boxed{4}\).