I interpret this as f(x)=x+3 when x<-2 and f(x)=-2x-3 when x>-2, because the whole domain of x is covered by one or other function. Treating the functions separately, the domain of the first function is all x<-2; the domain of the second function is all x>-2.
When x=0 we have the y or f(x) intercept and the second function applies, so the y intercept is -3.
When y=f(x)=0 the x intercepts are -3 when the first function applies (-3<-2), and -3/2 when the second function applies.
(-2)=1 and when x is just less than -2 f(x) approaches 1.
The slope of f(x) is positive (/) when x<-2 and negative (\) when x>-2. Therefore the graph represents an inverted V with apex at (-2,1) and it cuts the x axis at -3 and -3/2. The left part of the graph can be drawn by joining (-2,1) to (-3,0) and extending the line below the x axis where x<-3 and y<0; and the right part can be drawn by joining (-2,1) to (0,-3), cutting through the x axis at (-3/2,0) and extending the line below the x axis where x>0 and y continuing negative. The range is f(x)<1.