I am currently taking Calc III as an online course (yes, big mistake). I am at a section where we are evaluating the domains and ranges for functions with both x and y variables in it. As far as finding domains, no problem. However, the textbook doesn't explain how to solve for ranges with x and y components in a function very well. I am wondering if there's a specific method (steps) for doing so, or if it varies depending on the structure of the function? The example they used was they first solved for the domain, then manipulated that domain equation to get a part of it to look like the restricted portion of the original function to find the range. While it wasn't too difficult for that particular problem, it just seems like it would get really sloppy and challenging to do with more complex problems. I'm just wondering if there is a specific method or if it is sort of like a related rate problem where you really have to just analyze it and figure it out?