Use the formula f(b)−f(a)b−a

Question

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
.

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 find \( f(-2) \) and \( f(0) \).

Given the values from the table:

• \( f(-2) = 0 \)
• \( f(0) = 8 \)

Now, we can substitute these values into the 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 over the interval \([-2, 0]\) is:

\[ \boxed{4} \]