Graphing Greatest Integer Functions

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]

Graph the given function. 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]

Graph the given function. 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 = [x2]

Graph the given function. y = [x^2] (-2 <= x <= 2)

Lightly draw y = x2(-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 = [x2].