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
.
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:

$$\boxed{{\displaystyle 4}}$$