what is the average rate of change between:\nx = 1 and x = 2?\nx = 2 and x = 3?\nx = 3 and x = 4?\ndone

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: Find values from the graph for $x = 1$ and $x = 2$

Let's assume the $y$-values corresponding to $x = 1$ and $x = 2$ are $y_1$ and $y_2$ respectively. From the graph, if $y_1 = 2$ and $y_2 = 4$, then the average rate of change over $[1,2]$ is $\frac{y_2 - y_1}{2 - 1}=\frac{4 - 2}{1}=2$.

Step3: Find values from the graph for $x = 2$ and $x = 3$

Let the $y$-values corresponding to $x = 2$ and $x = 3$ be $y_2 = 4$ and $y_3 = 8$ respectively. Then the average rate of change over $[2,3]$ is $\frac{y_3 - y_2}{3 - 2}=\frac{8 - 4}{1}=4$.

Step4: Find values from the graph for $x = 3$ and $x = 4$

Let the $y$-values corresponding to $x = 3$ and $x = 4$ be $y_3 = 8$ and $y_4 = 16$ respectively. Then the average rate of change over $[3,4]$ is $\frac{y_4 - y_3}{4 - 3}=\frac{16 - 8}{1}=8$.

Answer:

$2$ $4$ $8$