Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $1leq xleq3$?

Explanation:

Step1: Find \( f(1) \) and \( f(3) \)

From the graph, \( f(1)=8 \) and \( f(3)= - 4 \)

Step2: Use the average rate of change formula

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 \(a = 1\), \(b = 3\), so \(\frac{f(3)-f(1)}{3 - 1}=\frac{-4 - 8}{3 - 1}\)

Step3: Calculate the value

\(\frac{-4 - 8}{3 - 1}=\frac{-12}{2}=-6\)

Answer:

\(-6\)