The given function is
[tex]f(x)=\begin{cases}\frac{1}{3}x+1\colon x<-2 \\ x-3\colon-1\leq x<2 \\ 3\colon x\ge2\end{cases}[/tex]A piecewise function is a function that behaves differently on each interval. In this case, we have three intervals with three different behaviors, so let's graph each of them.
We have to find coordinated points for the values x = -4 and x = -3. To do so, we have to evaluate the expression for each value.
[tex]\begin{gathered} \frac{1}{3}\cdot(-4)+1=-\frac{4}{3}+1=\frac{-4+3}{3}=-\frac{1}{3} \\ \frac{1}{3}\cdot(-3)+1=-1+1=0 \end{gathered}[/tex]So we have two points for the first expression: (-4, -1/3) and (-3, 0).
Let's evaluate the expression for x = -1 and x = 0.
[tex]\begin{gathered} -1-3=-4 \\ 0-3=-3 \end{gathered}[/tex]The points are (-1, -4) and (0, -3).
For the third part, we don't have to evaluate any expression because the function, in that interval, is a horizontal line.
Now, we just have to graph all the points on the same coordinated plane, as the image below shows.
