I have function f(x) and only know it has point x=a, which is a point of discontinuity(jump). Based on this information we can state:
There are 4 statements
- f(x) cannot have domain all Real numbers
- f(x) does not have right and left limit in point x=a
- f(x) does have in point x=a local minimum
- f(x) does not have limit in point x=a
Well, in my opinion, first statement is false, because sign(x) has point of discontinuity(jump) and does have all Real numbers as domain. Second is also false, because one sided limit exists situated to right/left side from "jump". Third is also false because it could be also local maximum since the jump is not specified. And the fourth is right, because when there is a jump, right and left limits are not equal and thus limit does not exist.
Am I right? Thx a lot.