The given piecewise-defined function is:
[tex]g(x)=\begin{cases}{2\qquad\text{ if }x<-1} \\ {3\qquad\text{ if }x=-1} \\ {-1\qquad\text{ if }x>-1}\end{cases}[/tex]
It is required to graph the function.
To do this, graph each piece with respect to the corresponding domain.
Graph g(x)=2 over x<-1:
Notice that an open circle is at x=-1 since it is not included in the interval x<-1.
Graph g(x)=3 for x=-1. This is just a point:
Finally, graph g(x)=-1 for x>-1:
There is an open circle at x=-1 since it is not included in the interval x>-1.
Thus, the required graph of the piecewise-defined function is shown below:
