what is the average rate of change of f(x) from x = -2 to x = 1?

Explanation:

Step1: Identify the formula

The formula for the average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 1$.

Step2: Determine the function - values

From the graph, when $x=-2$, $f(-2)=1$; when $x = 1$, $f(1)=7$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(1)-f(-2)}{1-(-2)}=\frac{7 - 1}{1+2}=\frac{6}{3}=2$.

Answer:

2