Question

question
given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 2 leq x leq 3 ).

( x )	( f(x) )
2	17
3	19
4	21

answer attempt 1 out of 2
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Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) over the interval \( [a, b] \) is given by \( \frac{f(b) - f(a)}{b - a} \). Here, \( a = 2 \), \( b = 3 \).

Step2: Identify \( f(2) \) and \( f(3) \) from the table

From the table, when \( x = 2 \), \( f(2)=17 \); when \( x = 3 \), \( f(3)=19 \).

Step3: Substitute into the formula

Substitute \( a = 2 \), \( b = 3 \), \( f(2)=17 \), and \( f(3)=19 \) into the formula: \( \frac{f(3)-f(2)}{3 - 2}=\frac{19 - 17}{3 - 2} \).

Step4: Simplify the expression

Calculate the numerator and denominator: \( \frac{2}{1}=2 \).

Answer:

2