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 8 ≤ x ≤ 9?
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, $a = 8$ and $b=9$.
Step2: Read function values from the graph
From the graph, when $x = 8$, $f(8)=0$. When $x = 9$, assume the value of $y$ (i.e., $f(9)$) is $50$ (by estimating from the graph's scale).
Step3: Calculate the average rate of change
Substitute $a = 8$, $b = 9$, $f(8)=0$, and $f(9)=50$ into the formula: $\frac{f(9)-f(8)}{9 - 8}=\frac{50-0}{1}=50$.
Answer:
$50$