Question

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 )?

(1) ( \frac{3}{4} )
(2) ( -2 )
(3) ( -\frac{1}{2} )
(4) ( -\frac{3}{2} )

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

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Answer:

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