1. find average rate of change over the interval 1,2. 2. find average rate of change over the interval 0,1…

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

Step2: For the interval $[1,2]$

Let's assume the function values at $x = 1$ and $x = 2$ are $f(1)$ and $f(2)$ respectively. First, find the values of the function from the graph at $x = 1$ and $x = 2$. Suppose $f(1)=y_1$ and $f(2)=y_2$. Then the average rate of change is $\frac{f(2)-f(1)}{2 - 1}=f(2)-f(1)=y_2 - y_1$.

Step3: For the interval $[0,1]$

Find the function values at $x = 0$ and $x = 1$, say $f(0)=y_0$ and $f(1)=y_1$. The average rate of change is $\frac{f(1)-f(0)}{1 - 0}=f(1)-f(0)=y_1 - y_0$.

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

Find the function values at $x=-2$ and $x = 0$, say $f(-2)=y_{-2}$ and $f(0)=y_0$. The average rate of change is $\frac{f(0)-f(-2)}{0-(-2)}=\frac{f(0)-f(-2)}{2}=\frac{y_0 - y_{-2}}{2}$.

Since we don't have the actual function - value data from the graph, we leave the answers in the general form based on the formula.

Answer:

1. For the interval $[1,2]$, the average rate of change is $f(2)-f(1)$.
2. For the interval $[0,1]$, the average rate of change is $f(1)-f(0)$.
3. For the interval $[-2,0]$, the average rate of change is $\frac{f(0)-f(-2)}{2}$.