Question

the average rate of change from x = -2 to x = 6 for the function shown in the graph is -2 -1/2 1/2 2

Explanation:

Step1: Recall average rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ from $x = x_1$ to $x = x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Identify the values of $x_1,x_2,f(x_1),f(x_2)$

Here, $x_1=-2$, $f(x_1) = 7$ (from point $B(-2,7)$), $x_2 = 6$, and $f(x_2)=3$ (from point $A(6,3)$).

Step3: Substitute values into the formula

$\frac{f(6)-f(-2)}{6-(-2)}=\frac{3 - 7}{6 + 2}$.

Step4: Simplify the expression

$\frac{3 - 7}{6 + 2}=\frac{-4}{8}=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$