The Floor Function and the Ceiling Function

Main Concept   The floor  of a real number x, denoted by $⌊x⌋$, is defined to be the largest integer no larger than x.   The ceiling of a real number x, denoted by $⌈x⌉$, is defined to be the smallest integer no smaller than x.   Graphs of the floor and ceiling functions

Use your mouse to draw a function $f$ and view the graphs of $⌊f\mathit{\(}x\mathit{\)}⌋$ and $⌈f\mathit{\(}x\mathit{\)}⌉$. Select what is displayed using the check boxes below the plot.

Notice that the function you draw always stays vertically between its floor and its ceiling.

Click on the plot to clear the graph, or drag again to clear and begin a new graph.