Question

consider the graph of f shown below. estimate the average rate of change from x = 2 to x = 5.

Explanation:

Step1: Recall 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, $a = 2$ and $b = 5$.

Step2: Estimate function values

From the graph, when $x = 2$, $y=f(2)\approx3$ and when $x = 5$, $y=f(5)\approx7$.

Step3: Calculate rate of change

Substitute into the formula: $\frac{f(5)-f(2)}{5 - 2}=\frac{7 - 3}{3}=\frac{4}{3}\approx1.33$.

Answer:

$\frac{4}{3}$