Question

the graph of a function g is shown below. use the graph of the function to find its average rate of change from x = -6 to x = -4. simplify your answer as much as possible.

Explanation:

Step1: Identify g(-6) and g(-4)

From the graph: $g(-6) = -2$, $g(-4) = 1$

Step2: Apply average rate formula

The average rate of change is $\frac{g(x_2)-g(x_1)}{x_2-x_1}$. Substitute $x_1=-6, x_2=-4$:
$\frac{g(-4)-g(-6)}{-4-(-6)} = \frac{1-(-2)}{-4+6}$

Step3: Simplify the expression

$\frac{1+2}{2} = \frac{3}{2}$

Answer:

$\frac{3}{2}$