Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -5 ≤ x ≤ 4?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-5$ and $b = 4$.

Step2: Find $f(-5)$ and $f(4)$ from the graph

From the graph, when $x=-5$, $f(-5)=-30$. When $x = 4$, $f(4)=-20$.

Step3: Calculate the average rate of change

Substitute $a=-5$, $b = 4$, $f(-5)=-30$ and $f(4)=-20$ into the formula: $\frac{f(4)-f(-5)}{4-(-5)}=\frac{-20-(-30)}{4 + 5}=\frac{-20 + 30}{9}=\frac{10}{9}$.

Answer:

$\frac{10}{9}$