given the function defined in the table below, find the average rate of change, in simplest form, of the…
given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 5 ≤ x ≤ 7. x f(x) 1 5 3 3 5 9 7 23
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b = 7$.
Step2: Identify $f(a)$ and $f(b)$
From the table, when $x=a = 5$, $f(5)=9$; when $x = b=7$, $f(7)=23$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(7)-f(5)}{7 - 5}=\frac{23 - 9}{2}$. Simplify the numerator: $23-9 = 14$. Then $\frac{14}{2}=7$.
Answer:
7