selected values of a function f are shown in the table above. what is the average rate of change of f over…

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 given by $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify $a$, $b$, $f(a)$ and $f(b)$

Here, $a = 1$, $b = 5$. From the table, when $x$ values are not given, assume the $x$ values are in order. So when $x = 1$, $f(1)=2$ and when $x = 5$, $f(5)=14$.

Step3: Calculate the average rate of change

Substitute $a = 1$, $b = 5$, $f(1)=2$ and $f(5)=14$ into the formula $\frac{f(b)-f(a)}{b - a}$, we get $\frac{f(5)-f(1)}{5 - 1}=\frac{14 - 2}{5 - 1}$.

Answer:

C. $\frac{14 - 2}{5 - 1}$