Greatest Integer Function: Graph

How to graph the greatest integer function on a coordinate plane: 2 examples and their solutions.

Example 1

Example

Solution

First, lightly draw y = x
on the coordinate plane.

Slope-Intercept Form

Draw full circles on the graph
where the y values are integers.

y = ..., -3, -2, -1, 0, 1, 2, 3, ...

Draw empty circles
under the full circles.
(under 1 unit)

If doable,
draw horizontal lines
between the full circle and the empty circle.

This is the graph of
y = [x].

Example 2

Example

Solution

First, lightly draw y = -(1/2)x + 1
on the coordinate plane.

Draw full circles on the graph
where the y values are integers.

y = ..., -3, -2, -1, 0, 1, 2, 3, ...

Draw empty circles
under the full circles.
(under 1 unit)

If doable,
draw horizontal lines
between the full circle and the empty circle.

This is the graph of
y = [-(1/2)x + 1].