Question

selected values of a function f are shown in the table above. what is the average rate of change of f over the interval 1,5?

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, \(a = 1\), \(b=5\), \(f(1)=2\), and \(f(5)=14\).

Step2: Substitute the values into the formula

Substitute \(a = 1\), \(b = 5\), \(f(1)=2\), and \(f(5)=14\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{14 - 2}{5-1}\).

Step3: Calculate the numerator and denominator

First, calculate the numerator: \(14−2=12\). Then, calculate the denominator: \(5 - 1=4\).

Step4: Simplify the fraction

Simplify \(\frac{12}{4}=3\).

Answer:

\(3\)