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) = x^2 + 6x + 8. Express your answer as an integer

Answer 1

To calculate 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 \( b = 0 \).

First, we need to calculate \( f(-2) \) and \( f(0) \):

1. Calculate \( f(-2) \):
\[
f(-2) = (-2)^2 + 6(-2) + 8
\]
\[
= 4 - 12 + 8 = 0
\]

2. Calculate \( f(0) \):
\[
f(0) = (0)^2 + 6(0) + 8
\]
\[
= 0 + 0 + 8 = 8
\]

Now, we can plug 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 \( f(x) \) over the interval \([-2, 0]\) is \( \boxed{4} \).