Basics on Greatest Integer Function

The greatest integer function is also called the floor function.

The greatest integer function or the floor function returns the first integer that is less than or equal to the given number.

In other words, the greatest integer function will round any number down to the nearest integer.

To be precise, here we are interested in the nearest integer below the given number.

The greatest integer function is represented by [x] or [x].

Examples

Consider y = [x].

• If we plug in 0.6 for x then y = [0.6] = 0

• If we plug in 0.98 for x then we get y = [0.98] = 0

• If we plug in 1 for x then we get y = [1] = 1

• If we plug in 1.9 for x then we get y = [1.9] = 1

Basically what we do here is just cut off the decimal part, BUT……..

If we plug in 0.99999999….for x with 9 recurring then y = [0.999999…….] = 1.

This is a rather strange thing…..this is because 0.99999999999999……. equals 1.

Now, let’s plug in a couple of negative numbers.

• If we plug in –0.6 for x then y = [–0.6] = –1

• If we plug in –1 for x then y = [–1] = –1

• If we plug in –1.7 for x then y = [–1.7] = –2

Consider y = [x – 2].

• If we plug in 2.6 for x then y = [2.6 – 2] = [0.6] = 0

• If we plug in 2.98 for x then we get y = [2.98 – 2] = [0.98] = 0

• If we plug in 2 for x then we get y = [2 – 2] = [0] = 0

Let’s plug in a couple of negative numbers.

• If we plug in –0.7 for x then y = [–0.7 – 2] = [– 2.7] = – 3

• If we plug in –1 for x then y = [–1 – 2] = [–3] = –3

The graph of y = [x – 2] is the graph of y = [x] moved to the right by 2 units.

Consider y = [x] – 3.

• If we plug in 3.6 for x then y = [3.6] – 3 = 3 – 3 = 0

• If we plug in 3.98 for x then we get y = [3.98] – 3 = 3 – 3 = 0

• If we plug in 3 for x then we get y = [3] – 3 = 3 – 3 = 0

Let’s plug in a couple of negative numbers.

• If we plug in –0.7 for x then y = [–0.7] – 3 = – 1 – 3 = –4

• If we plug in –1 for x then y = [–1] – 3 = –1 – 3 = –4

The graph of y = [x] – 3 is the graph of y = [x] moved down by 3 units.

For Your Practice

Find:

(1) [5.06]

(2) [0.99.........]

(3) [– 4.99999………]

Article Source: http://www.new.citynewslive.com

I’m Chandrajeet, an in-house writer for iCoachMath, the providing of All Free Solved Exampled for Math from K – 12. In All USA State Curriculum and also cover all Mathematics Curriculum topics & lessons. I am a regular reader and writer of Education articles.
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