what is the average rate of change between: x = 1 and x = 2? x = 2 and x = 3? x = 3 and x = 4? done y = mx +…
what is the average rate of change between: x = 1 and x = 2? x = 2 and x = 3? x = 3 and x = 4? done y = mx + b m = 1 b = 0 done
Answer
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 for $x = 1$ and $x = 2$
From the graph, assume $f(1)=2$, $f(2)=4$. Then the average rate of change is $\frac{f(2)-f(1)}{2 - 1}=\frac{4 - 2}{1}=2$.
Step3: Find values for $x = 2$ and $x = 3$
Assume $f(2)=4$, $f(3)=8$. Then the average rate of change is $\frac{f(3)-f(2)}{3 - 2}=\frac{8 - 4}{1}=4$.
Step4: Find values for $x = 3$ and $x = 4$
Assume $f(3)=8$, $f(4)=16$. Then the average rate of change is $\frac{f(4)-f(3)}{4 - 3}=\frac{16 - 8}{1}=8$.
Answer:
2 4 8