Concavity and Convexity of a piecewise function

Question

I am given the following two functions, and I am to figure out if they are concave.

I used the formula for determining if it is concave or convex. If my calculations are correct, this function is convex in certain cases and concave in certain different cases. My question is, then is this function both concave and convex? On the other hand, if it is strictly convex in a specific case is the function becomes convex because strictly convex dominates?

Thanks for the help guys

Answer 1

This function is neither concave or convex. As a side note, you do not need continuity for a function to be concave or convex.