use the functions shown in the graphs to find the average rate of change over the specified intervals. 1) a…

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: For the first function and interval [ - 5,0]

Estimate $f(-5)$ and $f(0)$ from the graph. Suppose $f(-5)=10$ and $f(0)= - 2$. Then the average rate of change is $\frac{f(0)-f(-5)}{0-(-5)}=\frac{-2 - 10}{5}=\frac{-12}{5}=-2.4$.

Step3: For the first function and interval [ - 5,2]

Estimate $f(-5)$ and $f(2)$. Suppose $f(-5)=10$ and $f(2)=1$. Then the average rate of change is $\frac{f(2)-f(-5)}{2-(-5)}=\frac{1 - 10}{7}=\frac{-9}{7}\approx - 1.29$.

Step4: For the first function and interval [2,5]

Estimate $f(2)$ and $f(5)$. Suppose $f(2)=1$ and $f(5)=-10$. Then the average rate of change is $\frac{f(5)-f(2)}{5 - 2}=\frac{-10 - 1}{3}=\frac{-11}{3}\approx - 3.67$.

Step5: For the second function and interval [ - 2,2]

Estimate $f(-2)$ and $f(2)$. Suppose $f(-2)=2$ and $f(2)=-4$. Then the average rate of change is $\frac{f(2)-f(-2)}{2-(-2)}=\frac{-4 - 2}{4}=\frac{-6}{4}=-1.5$.

Step6: For the second function and interval [4,7]

Estimate $f(4)$ and $f(7)$. Suppose $f(4)=8$ and $f(7)=6$. Then the average rate of change is $\frac{f(7)-f(4)}{7 - 4}=\frac{6 - 8}{3}=-\frac{2}{3}\approx - 0.67$.

Step7: For the second function and interval [0,4]

Estimate $f(0)$ and $f(4)$. Suppose $f(0)=-4$ and $f(4)=8$. Then the average rate of change is $\frac{f(4)-f(0)}{4 - 0}=\frac{8-(-4)}{4}=\frac{12}{4}=3$.

(Note: The values of $f(x)$ are estimated from the graph, and actual values may vary slightly depending on the accuracy of estimation.)