The function f(x)=-|x+3| is defined as follows:
for x+3≥0, that is for x≥-3, f(x)=-(x+3)=-x-3
for x+3<0, that is for x<-3, f(x)=-[-(x+3)]=x+3
Thus in the interval [-3, infinity) we draw the half line, or ray, (i) y=-x-3,
and in the interval (-infinity, -3) we draw the half line y=x+3.
To draw y=-x-3, we can use the points (-3, 0) and (0, -3),
to draw the line y=x+3 we can use the points (-3, 0) and (0, 3)
Notice that the points we used to draw the second line, are not in the domain of the line, that is why on (-3, infinity) the line is dashed, that is it does not exist there, but we can still use it for practical purposes of drawing the half line.