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Greatest integer function is a function that gives the greatest integer less than or equal to a given number. The greatest integer less than or equal to a number x is represented as ⌊x⌋.

The Greatest Integer Function is also known as the Floor Function. It is written as f(x) = ⌊x⌋ f (x) = ⌊ x ⌋. The value of ⌊x⌋ ⌊ x ⌋ is the largest integer that is less than or equal to x x.

The greatest integer functions (or step functions) can help us find the smaller integer value close to a given number. The step function’s graph can be determined by finding the values of y at certain intervals of x.

less than or equal to x. In essence, it rounds down a real number to the nearest integer. or find in the Catalog. • If copying the graph from your calculator, be sure to indicate the open and …

Apr 23, 2025 · Learn about the Greatest Integer Function (⌊x⌋), its definition, graph, properties, and solved examples. Understand how it works with step-by-step illustrations.

Three quick graphs involving the greatest integer function. The properties and characteristics of the Greatest Integer Function, its equation, and its graph. The greatest integer function (step function or floor function) Try out our new and fun Fraction Concoction Game.

The greatest integer function is denoted by y = [x] For all real values of x, the greatest integer function returns the greatest integer which is less than or equal to x. To graph the parent function y = [x], we have to substitute some random values for x. Substitute x = -3, -2, -1, 0, 1, 2, 3. y = [-3] = -3 ----> (-3, -3) y = [-2] = -2 ...

Last updated at Dec. 16, 2024 by Teachoo. Since y will have integer values ( … –3, –2, –1, 0, 1, 2, 3, …)

Jun 28, 2024 · Let’s understand the graph of the greatest integer function through a plot. Suppose f (x) = ⌊x⌋, if x is an integer, then the value of f will be x itself and if x is not an integer, then the value of x will be the integer just smaller than x. Example: For all numbers resting in the interval [0,1), the output of f will be 0. That is: