Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -7 ≤ x ≤ -2?

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, $a=-7$ and $b = - 2$.

Step2: Find $f(-7)$ and $f(-2)$ from the graph

From the graph, when $x=-7$, $y = f(-7)=-30$. When $x=-2$, $y = f(-2)=25$.

Step3: Calculate the average rate of change

Substitute $f(-7)=-30$, $f(-2)=25$, $a=-7$, and $b = - 2$ into the formula: $\frac{f(-2)-f(-7)}{-2-(-7)}=\frac{25-(-30)}{-2 + 7}=\frac{25 + 30}{5}=\frac{55}{5}=11$.

Answer:

$11$