Question

calculate an average rate of change from a graph use the graph to answer the question. what is the average rate of change from x = 0 to x = 18?

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 $b = 18$.

Step2: Determine $f(0)$ and $f(18)$ from the graph

From the graph, when $x = 0$, $y=f(0)=10$. When $x = 18$, $y = f(18)=4$.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 18$, $f(0)=10$ and $f(18)=4$ into the formula: $\frac{f(18)-f(0)}{18 - 0}=\frac{4 - 10}{18}=\frac{-6}{18}=-\frac{1}{3}$.

Answer:

$-\frac{1}{3}$