Sorry for no description of the type of question, but I'm so out to lunch on this stuff I don't even know what I'd call it. Ok, so I'm not looking for answers here, I'd just appreciate being pushed in the right direction. Suppose that f : R -> R is continuous and one-to-one (that is, x1 != x2 --> f(x1) != f(x2). Prove that for each interval I = [a,b] contained in R either f(I) = [f(a), f(b)] or f(I) = [f(b), f(a)]. I have no idea what to consider for this problem. Sorry for the bad notation. I'm not too proficient at latex.