Greatest Integer Function

Greatest Integer Function

f(x)=⟦x⟧

The Greatest Integer Function is also called the Step Function because the graph
resembles steps.

example: Suppose you make wallets and you charge $1 for every 2 pounds for shipping
with the first 2 pounds free. If a package weighs [0, 1.9] pounds you charge $0. If
it weighs [2, 3.9] pounds you charge $1. If it weighs [4, 5.9] pounds you charge $2
and so on. THe graph might look like this.

f(x)=⟦x⟧⟹the greatest integer less than or equal to x

Some values of the greatest integer function are as follows.
⟦-1⟧=(greatest integer < -1) = -1
⟦-½ ⟧=-1
⟦1/10⟧=0
⟦1.5⟧=1
⟦1.9⟧=1

Graph of the greatest integer function has the following characteristics

●Domain is the set of all real numbers

●Range is the set of all integers

●Y-intercept is the origin (0,0)

●X-intercepts in the interval [0,1)

●Is constant between consecutive integers

●Jumps vertically one unit at each integer

Value of x.

Multiple Choice

What is the value of $$\lfloor7.6\rfloor$$  

• 7

• 6

• 8

• 7.6

Multiple Choice

What is the value of $$\lfloor-3.4\rfloor$$  

• -2

• -3

• -4

• 0

Multiple Choice

What is the value of $$\lfloor5\rfloor$$  

• 4

• 5

• 6

• undefined

Multiple Choice

What is the value of $$\lfloor-9\rfloor$$  

• -9

• -10

• 0

• undefined