The punchline of first semester calculus is this: You learn a formula to find the slope of a function (well, of the tangent line) at a point. The slope at the top of a hill/bottom of a valley is 0. Set slope to 0 to find the tops and bottoms of things. (Maximize profit, etc.) Before that though, you learn about continuous functions (you can draw them without lifting your pen). So for range, you take a continuous chunk of that graph (e.g. y=1/x has two chunks), find it's top and bottom, and now you know the range for that chunk. Combine all the ranges (there might only be one chunk), and you have the range for the function. The calc kids are right. A lot of things get easier once you know calc. It's called precal for a reason. It's not its own subject, just prep for calc. Answer from waldosway on reddit.com