# Greatest integer function domain and range

- What Is the Greatest Integer Function?
- Greatest Integer and Fractional Part Functions
- Greatest Integer function Domain and Range with graph

## What Is the Greatest Integer Function?

The Greatest Integer Function

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Vertex: the point 0,0 unless domain is altered. Average rate of change: is constant on each straight line section ray of the graph. A step function or staircase function is a piecewise function containing all constant "pieces". The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. A step function is discontinuous not continuous. You cannot draw a step function without removing your pencil from your paper. We have seen many graphs that are expressed as single equations and are continuous over a domain of the Real numbers.

## Greatest Integer and Fractional Part Functions

Greatest Integer Function With Limits & Graphs

## Greatest Integer function Domain and Range with graph

Greatest Integer Function [X] indicates an integral part of the real number which is nearest and smaller integer to. It is also known as floor of X. In the above figure, we are taking the floor of the values each time. Note : In the above graph, the left endpoint in every step is blocked dark dot to show that the point is a member of the graph, and the other right endpoint open circle indicates the points that are not the part of the graph. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Are you looking forward to understand what is greatest integer function and its domain and range? How to draw its graph. How to solve examples on it? Then this post contain in depth explanation stay tuned. Many students get confused believing [— 0.

For example:. However, the output will always be an integer.

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The greatest integer function is defined for all real numbers. Hence, as per its definition, its domain is the set of real numbers. [math]\lfloor.

General - Graphing the Greatest Integer Function

The largest integer that is less than 2.