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
⌊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.
Greatest integer Function
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 ⌋.
Example 1: Find the best integer role for following
According to the best integer function definition
(a) ⌊-261⌋ = -261
(b) ⌊3.501⌋ = 3
(c) ⌊-1.898⌋ = -2
Example 2: Evaluate ⌊3.7⌋.
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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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