Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 1 leq x leq 2 ).

( x )	1	2	3	4

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 \( \frac{f(b) - f(a)}{b - a} \).

Step2: Identify the values of \( a \), \( b \), \( f(a) \), and \( f(b) \)

For the interval \( 1 \leq x \leq 2 \), we have \( a = 1 \), \( b = 2 \). From the table, \( f(1) = 9 \) and \( f(2) = 10 \).

Step3: Substitute the values into the formula

Substitute \( a = 1 \), \( b = 2 \), \( f(1) = 9 \), and \( f(2) = 10 \) into the formula:
\[
\frac{f(2) - f(1)}{2 - 1} = \frac{10 - 9}{2 - 1}
\]

Step4: Simplify the expression

Simplify the numerator and the denominator:
\[
\frac{10 - 9}{2 - 1} = \frac{1}{1} = 1
\]

Answer:

\( 1 \)