the average rate of change of g(x) between x = 4 and x = 7 is 5/6. which statement must be true? o…

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 $b = 7$, and the average rate of change is $\frac{5}{6}$.

Step2: Substitute values into formula

Substituting $a = 4$, $b = 7$ into the average - rate - of - change formula $\frac{g(b)-g(a)}{b - a}$, we get $\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}$.

Answer:

C. $\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}$