Hello!The graph is attached.Why?To solve the given piecewise function, we need to graph each of the functions that compound the main function with their respective domain restrictions.So, solving we have:- First function: Positive slope line (red line).[tex]f(x)=x+1=y\\\\y=x+1, if x<0[/tex]Let's find the axis intercepts in order to be able to graph the function.Finding the x-axis intercept, we need to make "y" equal to 0, so:[tex]y=x+1\\\\0=x+1\\x=-1[/tex]So, we have that the x-axis intercept is located at the point (-1,0)Finding the y-axis intercept, we to mate "x" equal to 0, so:[tex]y=x+1\\\\y=0+1\\y=1[/tex]So, we have that the y-axis intercept is located at the point (0,1)Hence, we have that the function exists from the values of "x" less than 0 to the negative infinite or (-∞,0)- Second function: Horizontal line (blue line).[tex]y=2,if0\leq x\leq 1[/tex]Since there is not variable, we know that it's a horizontal line that passes through y equal to 2.Hence, we have that the function exists between the values of "x" from 0 to 1 or [0,1]- Third function: Positive slope line (green line).[tex]y=x,ifx>0[/tex]Let's find the axis intercepts in order to be able to graph the function.Finding the x-axis intercept, we need to make "y" equal to 0, so:[tex]0=x+\\\\0=x+\\x=0[/tex]So, we have that the x-axis intercept is located at the point (0,0)Finding the y-axis intercept, we to make "x" equal to 0, so:[tex]y=x\\\\y=0\\y=0[/tex]We have that the function only pass through the point (0,0) or origin.Hence, we have that the function exists from the values of "x" greater than 2.So, the graph of the given function is attached.Have a nice day!