3. the table shows the values of a function g(x) for different values of x. which statement is true? a. the…

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

Step2: Check option a

For the interval $[-2,0]$, $a=-2$, $b = 0$, $g(-2)=14$, $g(0)=0$. Then $\frac{g(0)-g(-2)}{0-(-2)}=\frac{0 - 14}{2}=-7\neq - 14$.

Step3: Check option b

For the interval $[0,1]$, $a = 0$, $b=1$, $g(0)=0$, $g(1)=-7$. Then $\frac{g(1)-g(0)}{1 - 0}=\frac{-7-0}{1}=-7\neq7$.

Step4: Check option c

For the interval $[-2,1]$, $a=-2$, $b = 1$, $g(-2)=14$, $g(1)=-7$. Then $\frac{g(1)-g(-2)}{1-(-2)}=\frac{-7 - 14}{3}=\frac{-21}{3}=-7$.

Step5: Check option d

For the interval $[0,2]$, $a = 0$, $b=2$, $g(0)=0$, $g(2)=-10$. Then $\frac{g(2)-g(0)}{2 - 0}=\frac{-10-0}{2}=-5\neq\frac{1}{5}$.

Answer:

c. The average rate of change of the function $g(x)$ between $x = - 2$ and $x = 1$ is $-7$