Graph of the Floor Function $y = \lfloor x \rfloor$

$y = \lfloor x \rfloor$ returns the greatest integer not exceeding $x$ (also called the Gauss bracket).

• $\lfloor 2.7 \rfloor = 2$
• $\lfloor 3 \rfloor = 3$
• $\lfloor -1.2 \rfloor = -2$

The graph is a staircase that jumps up by $1$ at each integer, including the left end of each step but not the right. It is discontinuous at every integer.