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)

Answer 1

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

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

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

We start by finding the values of \( f(-2) \) 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 have:

• \( f(-2) = 0 \)
• \( f(0) = 8 \)

Next, we can apply these values in 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 \( f \) over the interval \([-2, 0]\) is:

\[ \boxed{4} \]