Question

the average rate of change of g(x) between x = 4 and x = 7 is $\frac{5}{6}$. which statement must be true?
$g(7)-g(4)=\frac{5}{6}$
$\frac{g(7 - 4)}{7 - 4}=\frac{5}{6}$
$\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}$
$\frac{g(7)}{g(4)}=\frac{5}{6}$

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is given by $\frac{g(b)-g(a)}{b - a}$. Here, $a = 4$ and $b = 7$.

Step2: Substitute values into formula

The average rate of change of $g(x)$ between $x = 4$ and $x = 7$ is $\frac{g(7)-g(4)}{7 - 4}$. Since the average rate of change is $\frac{5}{6}$, we have $\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}$.

Answer:

$\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}$ (the third option)