Question

a function g is shown below. use the graph of the function to find its average rate of change from x = - 3 to x = 1. simplify your answer as much as possible.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x=a$ to $x = b$ is given by $\frac{g(b)-g(a)}{b - a}$. Here, $a=-3$ and $b = 1$.

Step2: Read function values from the graph

From the graph, when $x=-3$, $g(-3)= - 5$ and when $x = 1$, $g(1)=-5$.

Step3: Calculate the average rate of change

Substitute the values into the formula: $\frac{g(1)-g(-3)}{1-(-3)}=\frac{-5-(-5)}{1 + 3}=\frac{-5 + 5}{4}=\frac{0}{4}=0$.

Answer:

$0$