Question

average rate of change quick check use the image to answer the question. use the average rate of change to describe the graph of f(x) over the interval 1,4. (1 point) the average rate of change is 3 the average rate of change is 1 the average rate of change is -1/3 the average rate of change is 1/3

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 $\frac{1}{3}$