1. 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.

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

5. 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

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

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

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 ]

9. 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)

10. Graph of the greatest integer function y =  x 

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

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

13. y =  x 

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

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

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