x+y is continuous everywhere and so is so is continous everywhere. is continuous for all positive x (and "continuous from the right" at x= 0) so is continuous for all (x,y) such that x+y> 0. x+ y= 0 or y= -x is a line through (0,0) and (1,0) has 1+ 0> 0 so is continuous "above and to the right" of that line.
is continous for (x,y) "above and to the right" of the line y= -x and "continuous from above and to the right:" on that line.