Question

the average rate of change for $-3\leq x\leq -0.3$ is \boxed{}. \
\
the average rate of change for the interval $-2\leq x\leq 0.333$ is

Explanation:

Step1: Recall average rate formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify points for $-3 \leq x \leq -0.3$

First, find $f(-3)$: At $x=-3$, the graph has $y=-2$. So $f(-3)=-2$.
Find $f(-0.3)$: At $x=-0.3$, the graph has $y=-3$. So $f(-0.3)=-3$.

Step3: Calculate for first interval

$$\frac{f(-0.3)-f(-3)}{-0.3 - (-3)} = \frac{-3 - (-2)}{-0.3 + 3} = \frac{-1}{2.7} \approx -0.37$$

Step4: Identify points for $-2 \leq x \leq 0.333$

$f(-2)=-4.5$ (given), $f(0.333)=1.85$ (given).

Step5: Calculate for second interval

$$\frac{f(0.333)-f(-2)}{0.333 - (-2)} = \frac{1.85 - (-4.5)}{0.333 + 2} = \frac{6.35}{2.333} \approx 2.72$$

Answer:

The average rate of change for $-3 \leq x \leq -0.3$ is $\approx -0.37$
The average rate of change for $-2 \leq x \leq 0.333$ is $\approx 2.72$