Use the formula f(b)−f(a)b−a

Question

to calculate the average rate of change over the interval [−2,−1]
given the function table for y=3x+2
. Express your answer as an integer.

x f(x)

−3
13

−2
1
−1
3
0 9(1 point)
The average rate of change is
.

Answer 1

To calculate the average rate of change of the function $f(x)=3x+2$ over the interval $[-2,-1]$, we can use the formula:

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

In this case, $a=-2$ and $b=-1$.

We first need to find $f(-2)$ and $f(-1)$:

1. From the function table:
   • $f(-2)=1$
   • $f(-1)=3$

Now, we can substitute these values into the formula:

$$\text{Average Rate of Change}=\frac{f(-1)-f(-2)}{-1-(-2)}$$

Calculating each part:

$$f(-1)-f(-2)=3-1=2$$ $$b-a=-1-(-2)=-1+2=1$$

Now substitute these results back into the formula:

$$\text{Average Rate of Change}=\frac{2}{1}=2$$

Thus, the average rate of change over the interval $[-2,-1]$ is:

$$\boxed{{\displaystyle 2}}$$