consider the graph of f shown below. estimate the average rate of change from x = 4 to x = 7.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b=7$.

Step2: Estimate function values from the graph

From the graph, when $x = 4$, $f(4)\approx3$; when $x = 7$, $f(7)\approx2$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(7)-f(4)}{7 - 4}=\frac{2 - 3}{3}=\frac{-1}{3}\approx - 0.33$.

Answer:

$-\frac{1}{3}$