Greatest integer duty Definition:

What is the biggest integer function? The greatest integer role is represented/denoted by ⌊x⌋, for any kind of real function. The role rounds -off the genuine number under to the integer less than the number. This function is likewise known together the Floor Function.

You are watching: The greatest integer function is defined by int(x) = the greatest integer that is

For eg:

⌊1.15⌋ = 1

⌊4.56567⌋ = 4

⌊50⌋ = 50

⌊-3.010⌋ = -4

Greatest integer role domain and range

The greatest features are characterized piecewise that domain is a team of actual numbers that are separated into intervals like <-4, 3), <-3, 2), <-2, 1), <-1, 0) and also so on.

Video Lesson

Greatest integer Function


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Greatest integer duty graph

When the intervals space in the type of (n, n+1), the value of best integer role is n, where n is an integer.

For example, the biggest integer role of the expression <3,4) will be 3.

The graph is no continuous. For instance, below is the graph the the duty f(x) = ⌊ x ⌋.

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Example Problems

Let’s Workout: 

Example 1: Find the best integer role for following

(a) -261

(b) 3.501

(c) ⌊-1.898⌋

Solution:

According to the best integer function definition

(a) ⌊-261⌋ = -261

(b) ⌊3.501⌋ = 3

(c) ⌊-1.898⌋ = -2

Example 2:  Evaluate ⌊3.7⌋.

See more: Answered: Silver Has An Atomic Radius Of Silver In Nm, Answered: Silver Has An Atomic Radius Of 0

Solution

On a number line, ⌊3.7⌋ lies between 3 and also 4

The biggest integer i beg your pardon is much less than 3.7 is 3.

So, ⌊3.7⌋ = 3 Answer!

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