Question

given the graph, find the average rate of change from x = 1 and x = 3. the average rate of change is

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$ and $b=3$.

Step2: Read function values from graph

From the graph, when $x = 1$, $y=f(1)= - 1$; when $x = 3$, $y=f(3)= - 3$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{-3-(-1)}{3 - 1}=\frac{-3 + 1}{2}=\frac{-2}{2}=-1$.

Answer:

$-1$