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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-5$ and $b = - 4$.

Step2: Read function values from the graph

From the graph, when $x=-5$, $f(-5)=-60$ (by looking at the $y$-value corresponding to $x = - 5$). When $x=-4$, $f(-4)=20$ (by looking at the $y$-value corresponding to $x=-4$).

Step3: Calculate the average rate of change

Substitute $a=-5$, $b = - 4$, $f(-5)=-60$ and $f(-4)=20$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(-4)-f(-5)}{-4-(-5)}=\frac{20-(-60)}{-4 + 5}=\frac{20 + 60}{1}=80$.

Answer:

$80$