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 ≤ 7?
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 $b = 7$.
Step2: Read function values from the graph
From the graph, find $f(5)$ and $f(7)$. Suppose $f(5)= - 4$ and $f(7)=4$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(7)-f(5)}{7 - 5}=\frac{4-(-4)}{2}=\frac{4 + 4}{2}=\frac{8}{2}=4$.
Answer:
4