1. Graphing Greatest Integer Functions

2. Step Functions – functions whose graphs resemble sets of stair steps.
Greatest Integer Function – the most notable step function
Notation of Greatest Integer Function : x
Meaning of Greatest Integer Function :
the greatest integer less than or
equal to x.

3. 2 2 ? 9 9 ? -3 -3 ? = = = Let’s evaluate some greatest integers…
the greatest integer less than or equal to x. -3 = -3 ?

4. 2.2 2 ? 1/2 ? -4.1 -5 ? = = = Let’s evaluate some greatest integers…
the greatest integer less than or equal to x.
1/2 = ?
-4.1 = -5 ? 1 2 3 -1 -2 -3 -4 -5

5. Let’s evaluate some greatest integers…
9.1 = ? 9
the greatest integer less than or equal to x.
51/3 = 5 ?
-22/9 = -3 ? 1 2 3 -1 -2 -3 -4 -5

6. x y
.25 .5
.75 1
1.25
1.5
1.75 2
Now that you know how to evaluate greatest integer functions, you can graph them.
y = x

7. Now that you know how to evaluate greatest integer functions, you can graph them.x y
.25 .5
.75 1
1.25
1.5
1.75 2
y = x +2

8. x y
.25 .5
.75 1
1.25
1.5
1.75 2
Now that you know how to evaluate greatest integer functions, you can graph them.
y = x - 4

9. x y
.25 .5
.75 1
1.25
1.5
1.75 2
Now that you know how to evaluate greatest integer functions, you can graph them.
y = -x + 2