text: college algebra: graph functions to answer domain,range, explanation?   graphically, a domain is how far across the x-axis a graph spans.  a range is how far up and down the y-axis a graph stretches.  some graphs, like y = x^2, are limited in range.  in this case, y can never be less than 0, so the range is y>=0.  x in this case can be anything, so the domain for x is all real numbers.  graphically that makes sense - you can graph your parabola as far left and right that you want to, but not up and down.  other graphs, like y = sin x, are even more limited in the y direction.  graphically, you can see that y can't go past -1 or 1, so the range is -1 <= y <= 1.  and still others have no bounds.  y = x exists everywhere - there's no limit on what x or y can be.  this is probably a lead-in to graphing more advanced functions, such as y = (x^2 - 1)/(x + 1), where you'll have a domain of all real values except for x = -1.  as you can tell, the function can't exist at x = -1 because you'll have a 0 denominator.  so graphically, you'll have problems with that.  (you'll end up drawing an open circle at that point to indicate that it doesn't exist there.)