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 -5 ≤ x ≤ 3?
Answer
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, $a=-5$ and $b = 3$.
Step2: Find $f(-5)$ and $f(3)$ from the graph
From the graph, when $x=-5$, $f(-5)=0$. When $x = 3$, assume $f(3)=- 10$ (by estimating the $y$-value on the graph at $x = 3$).
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(3)-f(-5)}{3-(-5)}=\frac{-10 - 0}{3 + 5}=\frac{-10}{8}=-\frac{5}{4}$.
Answer:
$-\frac{5}{4}$