Question

the graph of a function f 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 $f(-2)$ from graph

From the graph, when $x=-2$, $f(-2)=-9$

Step2: Identify $f(4)$ from graph

From the graph, when $x=4$, $f(4)=3$

Step3: Apply average rate formula

The average rate of change formula is $\frac{f(b)-f(a)}{b-a}$, where $a=-2$, $b=4$.
$\text{Average rate}=\frac{f(4)-f(-2)}{4-(-2)}=\frac{3-(-9)}{4+2}=\frac{12}{6}$

Step4: Simplify the fraction

$\frac{12}{6}=2$

Answer:

2