Question

the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = -3 and x = 6. use the line segment to determine the average rate of change of the function f(x) on the interval -3 ≤ x ≤ 6.

plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$, where $a=-3$ and $b = 6$.

Step2: Identify $f(a)$ and $f(b)$ from the graph

From the graph, when $x=-3$, assume $f(-3)=15$ (by looking at the $y$ - value of the function at $x = - 3$). When $x = 6$, assume $f(6)=-10$ (by looking at the $y$ - value of the function at $x = 6$).

Step3: Calculate the average rate of change

Substitute $a=-3$, $b = 6$, $f(-3)=15$ and $f(6)=-10$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(6)-f(-3)}{6-(-3)}=\frac{-10 - 15}{6 + 3}=\frac{-25}{9}=-\frac{25}{9}$.

Answer:

$-\frac{25}{9}$