Limit of 2-branch function, point offset: , where

When a function has different branches on either side of the point of interest, we can determine the one-sided limits and see if they satisfy the Theorem of Limits.

Limit from the left:

Limit from the right:

Since , we conclude from the Theorem of Limits thatalso.

Note that the fact that the value of the function at x = 2 need not equal the limit there.