Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $1leq xleq2$.

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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, \(a = 1\) and \(b=2\).

Step2: Substitute the values into the formula

We know that \(f(1)=9\) and \(f(2) = 10\). Substituting these values into the formula \(\frac{f(2)-f(1)}{2 - 1}\), we get \(\frac{10 - 9}{2-1}\).

Step3: Simplify the expression

\(\frac{10 - 9}{2-1}=\frac{1}{1}=1\).

Answer:

\(1\)