jump.
f(x) = 2x+1 everywhere except x=3.
Since the limit from both sides is 7, but f(3)=6, there's no way to remove that break.
What kind of discontinuity is this piecewise function? Removable or jump?
f(x) ={ (2x^2 - 5x - 3)/(x-3) if x does not equal 3
............6............................if x = 3
4 answers
I thought that since the limit exists, but does not equal f(3) it would be removable
It is only removable if f(x) is defined to be the same as the limit value. If f(x) were 7 at x=3, then that would plug the hole. But since it is defined to be a different value, it creates a jump which cannot be joined to fill the hole.
Thank you so much for explaining that!
2 answers