#10\n4. find average rate of change over the interval -6,-2.\n5. find average rate of change over the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. We need to read the function values $f(a)$ and $f(b)$ from the graph.

Step2: For the interval $[-6,-2]$

From the graph, when $x=-6$, $y = - 3$ (i.e., $f(-6)=-3$), and when $x = - 2$, $y=2$ (i.e., $f(-2)=2$). Then the average rate of change is $\frac{f(-2)-f(-6)}{-2-(-6)}=\frac{2 - (-3)}{-2 + 6}=\frac{5}{4}$.

Step3: For the interval $[-2,0]$

When $x=-2$, $y = 2$ (i.e., $f(-2)=2$), and when $x = 0$, $y=3$ (i.e., $f(0)=3$). Then the average rate of change is $\frac{f(0)-f(-2)}{0-(-2)}=\frac{3 - 2}{2}=\frac{1}{2}$.

Step4: For the interval $[0,2]$

When $x = 0$, $y=3$ (i.e., $f(0)=3$), and when $x = 2$, $y=3$ (i.e., $f(2)=3$). Then the average rate of change is $\frac{f(2)-f(0)}{2-0}=\frac{3 - 3}{2}=0$.

Step5: For the interval $[2,5]$

When $x = 2$, $y=3$ (i.e., $f(2)=3$), and when $x = 5$, $y=6$ (i.e., $f(5)=6$). Then the average rate of change is $\frac{f(5)-f(2)}{5 - 2}=\frac{6 - 3}{3}=1$.

Step6: For the interval $[-6,5]$

When $x=-6$, $y=-3$ (i.e., $f(-6)=-3$), and when $x = 5$, $y=6$ (i.e., $f(5)=6$). Then the average rate of change is $\frac{f(5)-f(-6)}{5-(-6)}=\frac{6-(-3)}{5 + 6}=\frac{9}{11}$.

Answer:

4. $\frac{5}{4}$
5. $\frac{1}{2}$
6. $0$
7. $1$
8. $\frac{9}{11}$