when the function defined in the table below, find the average rate of change of the function over the…

when the function defined in the table below, find the average rate of change of the function over the interval 5 ≤ x ≤ 7.\n\n| x | f(x) |\n|----|----|\n| 1 | 26 |\n| 3 | 12 |\n| 5 | 6 |\n| 7 | 8 |

when the function defined in the table below, find the average rate of change of the function over the interval 5 ≤ x ≤ 7.\n\n| x | f(x) |\n|----|----|\n| 1 | 26 |\n| 3 | 12 |\n| 5 | 6 |\n| 7 | 8 |

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, $a = 5$, $b = 7$, $f(a)=f(5) = 6$, and $f(b)=f(7)=8$.

Step2: Substitute values into formula

$\frac{f(7)-f(5)}{7 - 5}=\frac{8 - 6}{2}$

Step3: Simplify the expression

$\frac{2}{2}=1$

Answer:

$1$