1. The Greatest Integer Function: GIF
World 3-1
The Greatest Integer Function: GIF

2. f(x) = [x] output input The simplest greatest integer function,
GIF for short is….
f(x) = [x]
output
input
Square brackets [ ] always mean round down to
the nearest integer. THINK FLOOR
Eg 1.
f(x) = [x]
f(3.5) = [3.5]
f(3.99) = [3.99]
f(3) = [3]
= 3
= 3
= 3

3. -1 1 2 -2 -3 3 Eg 2. Evaluate f(x)= [x] f(4) = [4.4] f(-6) = [-6]
= 4
= -6
= -6
= -8 -1 1 2 -2 -3 3
Imagine a number line. The GIF always shift the value
left, to the nearest integer.

4. Eg. 3 Evaluate the GIF’s with transformations
g(x) = 2[x] +1
s(x) = 5[x-0.3] - 8
g(1.2) = 2[1.2] +1
s(3.2) = 5[ ] -8
= 2(1) + 1
= 5[2.9] - 8
= 3
= 5(2) - 8
= 2
u(x) = 8[0.4x] - 2
w(x) = -3[-4x] - 27
u(5) =
8[0.4(5.1)] -2
w(2.1) =
-3[(-4)(2.1)] - 27
= 8[2.04] -2
= -3[-8.4] - 27
= 8(2) -2
= -3(-9) - 27
= 14 =
= 0

5. Eg. 4 Given the output, f(x), the input, x, can be solved
If [x] = i, and i is an integer, then
[x+3] = -2
[x] = 4
x + 3 ≥ -2
x ≥ 4
x < 4 + 1
x + 3 <
x < 5
x ≥ -5
x < -4

6. Eg. 5 Solve for x
[-2x] = 4
2[x-4] = 10
[-2x] < 4+1
[-2x] ≥ 4
2[x-4] ≥ 10
2[x-4] < 10
-2x < 5 2 2 2
-2x ≥ 4 2 -2 -2 -2 -2
[x-4] < 5 +1
[x-4] ≥ 5
x ≤ -2
x > -2
x – 4 ≥ 5
x-4 < 6
+ 4
+ 4
+ 4
+ 4
x ≥ 9
x < 10
Math Gods say flip sign when dividing by a negative

7. Homework
Activity 1
Pg. 117 #1-5
Pg. 116 Act 1 #1