# Greatest Integer Function: Graph

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

## ExampleGraph y = [x]

Solution

Solution (Detail)

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].

## ExampleGraph y = [-(1/2)x + 1]

Solution

Solution (Detail)

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].