Question

What kind of discontinuity is this:

F(x)= (2x^2 - 5x -3)/(x-3) if x does not equal 3
6 if x=3

It is a pieces use function.

I thought it was removable but my answer key says it is a jump discontinuity. This is from an exam review and I want to get it right.

Answer 1

I meant to say it is a piecewise function

Answer 2

everywhere except x=3, F(x) = 2x+1

Since 6≠7 you have a jump there. The limit from both sides is 7, but F is defined to be 6, and there's no way to close that gap.