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 = 2 to x = 10? -8, $\frac{1}{8}$, 8, -$\frac{1}{8}$

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, $a = 2$ and $b = 10$.

Step2: Find $f(2)$ and $f(10)$ from the graph

From the graph, when $x = 2$, $y=f(2)=7$; when $x = 10$, $y = f(10)=6$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(10)-f(2)}{10 - 2}=\frac{6 - 7}{8}=\frac{-1}{8}=-\frac{1}{8}$.

Answer:

$-\frac{1}{8}$