Question

the graph of a function h is shown below. use the graph of the function to find its average rate of change from x=-2 to x=4. simplify your answer as much as possible.

Explanation:

Step1: Identify $h(-2)$ from graph

From the graph, when $x=-2$, $h(-2)=3$.

Step2: Identify $h(4)$ from graph

From the graph, when $x=4$, $h(4)=-9$.

Step3: Apply average rate formula

The average rate of change formula is $\frac{h(x_2)-h(x_1)}{x_2-x_1}$. Substitute $x_1=-2$, $x_2=4$, $h(x_1)=3$, $h(x_2)=-9$:
$\frac{h(4)-h(-2)}{4-(-2)}=\frac{-9-3}{4+2}$

Step4: Simplify the expression

Calculate numerator and denominator:
$\frac{-12}{6}=-2$

Answer:

$-2$