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 2 ≤ x ≤ 7? answer attempt 1 out of 2
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, $a = 2$ and $b=7$.
Step2: Read function values from the graph
From the graph, when $x = 2$, $y=f(2)\approx - 5$. When $x = 7$, $y=f(7)\approx40$.
Step3: Calculate the average rate of change
Substitute $f(2)\approx - 5$, $f(7)\approx40$, $a = 2$, and $b = 7$ into the formula: $\frac{f(7)-f(2)}{7 - 2}=\frac{40-(-5)}{5}=\frac{40 + 5}{5}=\frac{45}{5}=9$.
Answer:
9