Observe the graph:

The parent function is greatest integer function $\"\"$ .

With a greatest integer function, more than one transformation can lead to the same graph of $\"\"$ .

One possibility is a dilation with no shift at all.

The point $\"\"$ is on the graph of $\"\"$ .

Use the point $\"\"$ to determine if there is a dilation.

Let $\"\"$ represent the dilation and solve for $\"\"$ .

$\"\"$

The function is $\"\"$ .

$\"\"$ .