Question

The graph of a function is given.

Determine (a) the net change and (b) the average rate of change between the indicated points on the graph.

Short answer

Net change = 2

Average rate of change =$\frac{2}{3}$

Step-by-step solution

Given Information

The graph of the given function,

Part (a) Step 1: Calculate Net change

From the graph we have, $(1,3)$and $(4,5)$.

For a net change, $f\left(4\right)-f\left(1\right)$

$$\begin{gathered} =5-3 \\ =2 \end{gathered}$$

part (b) Step 1: Calculate average rate change

From the graph we have, $(1,3)$and $(4,5)$.

Average rate of change,$=\frac{f\left(4\right)-f\left(1\right)}{4-1}$

$$\begin{gathered} =\frac{5-3}{4-1} \\ =\frac{2}{3} \end{gathered}$$