31. what is the average rate of change in f(x) on the interval 5,9? a - 1/2 b 5/4 c 4 d -6 31 of 36

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify $a$, $b$, $f(a)$ and $f(b)$ from the graph

Let $a = 5$, $b = 9$. From the graph, when $x = 5$, $f(5)=8$; when $x = 9$, $f(9)=3$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(9)-f(5)}{9 - 5}=\frac{3 - 8}{9 - 5}=\frac{-5}{4}=-\frac{5}{4}$.

Answer:

A. $-\frac{5}{4}$