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.