average rate of change quick check use the image to answer the question. use the average rate of change to…

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$ and $b=4$.

Step2: Determine function values from graph

From the graph, when $x = 1$, $f(1)=1$ and when $x = 4$, $f(4)=2$.

Step3: Calculate average rate of change

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

Answer:

The average rate of change is $\frac{1}{3}$