question 14 based on the graph above, estimate (to one decimal place) the average rate of change from x = 1…

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$ and $b = 3$.

Step2: Estimate function values from graph

From the graph, when $x = 1$, $y=f(1)\approx7$; when $x = 3$, $y=f(3)\approx3$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{3 - 7}{2}=\frac{-4}{2}=-2.0$

Answer:

$-2.0$