# How do you find discontinuity of a piecewise function?

##### 1 Answer

In most cases, we should look for a discontinuity at the point where a piecewise defined function changes its formula. You will have to take one-sided limits separately since different formulas will apply depending on from which side you are approaching the point. Here is an example.

Let us examine where

Notice that each piece is a polynomial function, so they are continuous by themselves.

Let us see if

Since both limits give 1,

Since

Let us see if

Since the limits above are different,

Hence, there is a jump discontinuity at

I hope that this was helpful.