the graph of a function is given. (a) determine the net change between the indicated points on the graph…

Explanation:

Step1: Identify function values

Let the first - point be $(x_1,y_1)=(1,4)$ and the second - point be $(x_2,y_2)=(5,3)$.

Step2: Calculate net change

The net change of a function $y = f(x)$ between $x = x_1$ and $x = x_2$ is $\Delta y=f(x_2)-f(x_1)$. Here, $\Delta y=y_2 - y_1=3 - 4=-1$.

Step3: Calculate average rate of change

The average rate of change of a function $y = f(x)$ between $x = x_1$ and $x = x_2$ is $\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Substitute $x_1 = 1,x_2 = 5,y_1 = 4,y_2 = 3$ into the formula: $\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 4}{5 - 1}=\frac{-1}{4}=-\frac{1}{4}$.

Answer:

(a) -1 (b) $-\frac{1}{4}$