Question

What is the end behavior of the greatest integer function?

Answer 1

The end behavior is `y=x`. The left end goes to `-oo` and the right end goes to `oo`.

As `x` gets large positively or negatively, the decimal part becomes very small. If you extend the below graph, you should see that it looks like `y=x`. Another name for the greatest integer function is the floor function.

Note that desmos doesn't draw open circles on the right end of the line segments.