# Graphing Greatest Integer Functions

How to graph the given greatest integer functions on the coordinate plane: examples and their solutions.

## Example 1: Graph *y* = [*x*]

Lightly draw *y* = *x*

on the coordinate plane.

Draw full points on the line

where the *y* values are integers.

For each [point],

if the either adjacent points are lower than [the point],

draw an empty point

1 unit right below [the point].

For each [point] on *y* = *x*,

the left point is lower than [the point].

So, for each point,

draw an empty point

1 unit below [the point].

Draw horizontal lines

that connect the points with the same *y* value.

Then this is the graph of *y* = [*x*].

As you can see,

this graph looks like a step.

This is why

the [greatest integer function] is also called as

the [step function].

## Example 2: Graph *y* = [(-1/2)*x* + 1]

Lightly draw *y* = (-1/2)*x* + 1

on the coordinate plane.

Slope-intercept form

Draw full points on the line

where the *y* values are integers.

For each [point],

if the either adjacent points are lower than [the point],

draw an empty point

1 unit right below [the point].

For each [point] on *y* = (-1/2)*x* + 1,

the right point is lower than [the point].

So, for each point,

draw an empty point

1 unit below [the point].

Draw horizontal lines

that connect the points with the same *y* value.

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

## Example 3: Graph *y* = [*x*^{2}]

Lightly draw *y* = *x*^{2}(-2 ≤ *x* ≤ 2)

on the coordinate plane.

Draw full points on the line

where the *y* values are integers.

For each [point],

if the either adjacent points are lower than [the point],

draw an empty point

1 unit right below [the point].

At (0, 0), there are no adjacent points

that are lower than the point (0, 0).

So don't draw an empty point at (-1, 0).

Draw horizontal lines

that connect the points with the same *y* value.

Then this is the graph of *y* = [*x*^{2}].