1. for the function shown in the table below, which of the following is its average rate of change over the…

1. for the function shown in the table below, which of the following is its average rate of change over the interval ( 2 leq x leq 10 )?\n(1) ( \frac{3}{4} )\n(2) ( -2 )\n(3) ( -\frac{1}{2} )\n(4) ( -\frac{3}{2} )

1. for the function shown in the table below, which of the following is its average rate of change over the interval ( 2 leq x leq 10 )?\n(1) ( \frac{3}{4} )\n(2) ( -2 )\n(3) ( -\frac{1}{2} )\n(4) ( -\frac{3}{2} )

Answer

Explanation:

Step1: Recall the formula for average rate of change

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}). Here, (a = 2) and (b=10).

Step2: Identify (f(a)) and (f(b)) from the table

When (x = 2), (f(2)=9); when (x = 10), (f(10)=- 3).

Step3: Substitute into the formula

[ \begin{align*} \frac{f(10)-f(2)}{10 - 2}&=\frac{-3-9}{10 - 2}\ &=\frac{-12}{8}\ &=-\frac{3}{2} \end{align*} ]

Answer:

(4) (-\frac{3}{2})