Question

this is a multi - part item. the graph shows a function with rates of change calculated between x = 1 and x = 2 and between x = 3 and x = 4. what is the rate of change between x = 2 and x = 3?

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $y = f(x)$ between $x=a$ and $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. We need to estimate the function values at $x = 2$ and $x=3$ from the graph. Let's assume the function is $y=f(x)$. If we estimate $f(2)$ and $f(3)$ from the graph and use the formula for the average rate of change $\text{Rate of change}=\frac{f(3)-f(2)}{3 - 2}=f(3)-f(2)$.

Step2: Estimate function values

Suppose from the graph, $f(2)=4$ and $f(3)=8$. Then the rate of change $\frac{f(3)-f(2)}{3 - 2}=\frac{8 - 4}{1}=4$.

Answer:

4