Question

consider the graph of $f(x)$. what is the average rate of change of $f(x)$ from $x_1 = 0$ to $x_2 = 7$? please write your answer as an integer or simplified fraction.

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 \(x_1=0\), \(f(0) = 6\) (the point \((0,6)\)), and when \(x_2 = 7\), \(f(7)=12\) (the point \((7,12)\)).

Step3: Substitute the values into the formula

Substitute \(x_1 = 0\), \(f(x_1)=6\), \(x_2 = 7\), and \(f(x_2)=12\) into the formula: \(\frac{f(7)-f(0)}{7 - 0}=\frac{12 - 6}{7}\).

Step4: Simplify the fraction

\(\frac{12 - 6}{7}=\frac{6}{7}\).

Answer:

\(\frac{6}{7}\)