question the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on…
question 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 ≤ 5?
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 $b = 5$.
Step2: Estimate function values from the graph
From the graph, when $x=-5$, $f(-5)\approx - 16$. When $x = 5$, $f(5)\approx16$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(5)-f(-5)}{5-(-5)}=\frac{16-(-16)}{5 + 5}=\frac{16 + 16}{10}=\frac{32}{10}=3.2$.
Answer:
$3.2$