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
. Express your answer as an integer.

x f(x)

−3
−1

−2
0
−1
3
0 8
(1 point)
The average rate of change is
.
Remaining Attempts : 3

Answer 1

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

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

Where \( a = -2 \) and \( b = 0 \).

From the provided table, we have:

- \( f(-2) = 0 \)
- \( f(0) = 8 \)

Now, plug these values into the formula:

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

Substituting the function values:

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

Thus, the average rate of change over the interval \([-2, 0]\) is:

\[
\boxed{4}
\]