home > spring 2025 math 0999 - 01: support\nhomework 3.3: rates of change and behavior of graphs\nscore…

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$ and $b=2$.

Step2: Find $f(0)$ and $f(2)$ from the graph

From the graph, when $x = 0$, $f(0)=1$; when $x = 2$, $f(2)=5$.

Step3: Calculate the average rate of change

Substitute $f(0)=1$, $f(2)=5$, $a = 0$, and $b = 2$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(2)-f(0)}{2-0}=\frac{5 - 1}{2}=\frac{4}{2}=2$.

Answer:

2