the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
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 ≤ 1?
Answer
Answer:
$2$
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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-9$ and $b = 1$.
Step2: Find $f(-9)$ and $f(1)$ from the graph
From the graph, when $x=-9$, $f(-9)=-12$; when $x = 1$, $f(1)=8$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(1)-f(-9)}{1-(-9)}=\frac{8-(-12)}{1 + 9}=\frac{8 + 12}{10}=\frac{20}{10}=2$.