Well, you are only crazy if you expect a computer to be as good as your brain! What is graphed there is NOT the function you give. What is true is that
which is not defined at x= 1 and so its graph should have no point on the vertical line at x= 1.
However, for all x except x= 1,
which is defined at x= 1. The computer, calculating values at a finite number of values of x, "misses" the problem at x= 1 and just graphs y= 1/(x+1).
The graph is wrong.