what is the average rate of change of the function from x = 1 to x = 5? x 0 1 2 3 4 5 f(x) 12 7 2 15 18 21…
what is the average rate of change of the function from x = 1 to x = 5? x 0 1 2 3 4 5 f(x) 12 7 2 15 18 21 4.25 3.5 14 7 3
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$ and $b = 5$.
Step2: Find $f(1)$ and $f(5)$ from the table
From the table, when $x = 1$, $f(1)=7$; when $x = 5$, $f(5)=21$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(5)-f(1)}{5 - 1}=\frac{21 - 7}{4}=\frac{14}{4}=3.5$.
Answer:
3.5