You're right for a composition f's range is the domain of g....so for example, let:
Then the range of f is then since g is composed with f, (also written ) it's domain is the range of f, [-2,4]. Then the range of g is
So we have and and for a compostion you need only know the domain of to know all other domains/ranges.
However, the best appraoch to graphing would be to write out the composition as a single expression, e.g: then choose a set of points from your domain e.g: , calculate a table of values, plot the points and interpolate them into a smooth curve...just as you would with the graph of a normal function.
EDIT: Hmmm.. can someone please tell me the LaTeX for the composition symbol, the little circle? I thoubht it was: \circ
... I also tried \o and \O, but they didn't work either.