Question

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

Answer 1

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.

Answer 2

I thought that since the limit exists, but does not equal f(3) it would be removable

Answer 3

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.

Answer 4

Thank you so much for explaining that!