Question

consider the graph of ( f(x) ).
what is the average rate of change of ( f(x) ) from ( x_1 = 4 ) to ( x_2 = 7 )? please write your answer as an integer or simplified fraction.
answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x_1\) to \(x_2\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Step2: Identify the values of \(f(x_1)\) and \(f(x_2)\)

From the graph, when \(x_1 = 4\), \(f(4)=10\); when \(x_2 = 7\), \(f(7)=14\).

Step3: Substitute the values into the formula

Substitute \(x_1 = 4\), \(x_2 = 7\), \(f(x_1)=10\), and \(f(x_2)=14\) into \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). We get \(\frac{14 - 10}{7-4}\).

Step4: Simplify the expression

\(\frac{14 - 10}{7-4}=\frac{4}{3}\)

Answer:

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