Why do convex and concave function have their own name like that not the opposite? Here is the definition for each kind of function < And here is the definition for the words "concave and convex" in dictionary, with convex means curving out and concave means curving in. < In my logic, the convex function should be called concave func, and concave the opposite, because from the graph, I see a rumble strip bar, going up a little bit and down, like a concave function, but I think the rumble strip bar is described as "convex", here it's a little difficult for you to see my logic about it, but I don't understand why we call those function like that, not the opposite. Sorry because i'm not in an English speaker country. Thanks for your explaination!

I don't know the historical origins of the mathematical usage, but I have always thought it was backward also, and I'm a native speaker of English. The terms in mathematics are relative not to the x-axis, but to a horizontal line _above_ the curve (at $y=\infty$ if you like).

To avoid confusion, I think it's often better to use the terms "concave up" and "concave down", which are quite clear ("convex" = "concave up", and "concave" = "concave down").