A step function has the same y-value for several x-values and then steps up or down to another y-value.  The graph looks like stair steps.

The circles in the graph show this is still a function (only 1 y-value for each x).

One of the most common step functions is called the greatest integer function. y =  x  means y is the greatest integer less than or equal to x

So …  3.2  =  4.7  =  19.002  =  52.99999  =  6  =  .36  =  -7/275  =

So …  3.2  = 3  4.7  = 4  19.002  = 19  52.99999  = 52  6  = 6  .36  = 0  -7/275  = -8

NOTE: While your book uses the notation NOTE: While your book uses the notation y =  x  it is also standard to write y = [ x ]

NOTE: While your book uses the notation NOTE: While your book uses the notation y =  x  it is also standard to write y = [ x ] or 𝑦= 𝑥 or y = INT(x)

Graph of the greatest integer function y =  x 

y =  x  is often called the floor function (which is where the notation comes from) because it always rounds down to the previous integer.

A similar function y =  x  is called the ceiling function and always rounds up to the next integer.

y =  x 

You can also create more complicated floor and ceiling functions such as y =  x  + 1

The current cost to mail a letter is. y =. 47 + The current cost to mail a letter is y = .47 + .21  x – 1  How much does it cost to mail a letter that weighs 2.4 ounces?

The current cost to mail a letter is. y =. 47 + The current cost to mail a letter is y = .47 + .21  x – 1  How much does it cost to mail a letter that weighs 2.4 ounces? y = .47 + .21 * 2 = .89