Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $4\leq x\leq7$?

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 4\) and \(b=7\).

Step2: Find \(f(4)\) and \(f(7)\) from the graph

From the graph, when \(x = 4\), \(f(4)=30\); when \(x = 7\), \(f(7)= - 20\).

Step3: Substitute values into the formula

Substitute \(a = 4\), \(b = 7\), \(f(4)=30\), and \(f(7)=-20\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{f(7)-f(4)}{7 - 4}=\frac{-20 - 30}{7 - 4}\).

Step4: Calculate the result

\(\frac{-20-30}{7 - 4}=\frac{-50}{3}\approx - 16.67\)

Answer:

\(-\frac{50}{3}\)