We need to graph a piecewise function, there are two expressions and we need to respect the correct intervals.
For negative values of "x", the expression is "y=3", therefore this graph is a constant line at -3.
We need to insert a opened dot at "x=0", because the signal used is "<".
For positive values and for "x=0", we need to use the expression "x+1". This is a linear equation, to graph it, we need to find two points. We will look for the points at which "x = 0" and x"=1". We have:
[tex]\begin{gathered} f(0)=0+1=1 \\ f(1)=1+1=2 \end{gathered}[/tex]
We need to mark these two points at the graph and draw the line between them:
