Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -9 ≤ x ≤ -4?

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-9$ and $b = - 4$.

Step2: Estimate function values from graph

From the graph, when $x=-9$, assume $f(-9)=-10$ (by estimating the $y$ - value at $x = - 9$). When $x=-4$, assume $f(-4)=-2$ (by estimating the $y$ - value at $x=-4$).

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(-4)-f(-9)}{-4-(-9)}=\frac{-2-(-10)}{-4 + 9}=\frac{-2 + 10}{5}=\frac{8}{5}=1.6$.

Answer:

$1.6$