Which function is used to find the largest integer less than or equal to a specific value?

Read this section for an introduction to combinations of functions, then work through practice problems 1-9.

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Greatest Integer Function: [x] or INT(x)
How do you find the greatest integer less than or equal?
Which function returns the largest integer that is less than or equal to its argument?
What is the largest integer function?

Greatest Integer Function: [x] or INT(x)

The greatest integer function of a number

, is the largest integer which is less than or equal to . The value of is always an integer and is always less than or equal to . For example, , and . If is positive, then truncates (drops the fractional part of ) to get . If is negative, the situation is different: since is not less than or equal to and . On some calculators and in many programming languages the square brackets are used for grouping objects or for lists, and the greatest integer function is represented by .

Definition of : = the largest integer which is less than or equal to

The domain of The is all real numbers. The range of is only the integers. The graph of is shown in Fig. 14. It has a jump break, a step, at each integer value of , and is called a step function. Between any two consecutive integers, the graph is horizontal with no breaks or holes. The greatest integer function is useful for describing phenomena which change values abruptly such as postage rates as a function of the weight of the letter ("26¢ for the first ounce and 13¢ additional for each additional half ounce"). It can also be used for functions whose graphs are "square waves" such as the on and off of a flashing light.

Example 6: Graph .

Solution: One way to create this graph is to first graph , the thin curve in Fig. 15, and then apply the greatest integer function to y to get the thicker "square wave" pattern. <img src="https://learn.saylor.org/pluginfile.php/3596809/mod_book/chapter/20594/Screenshot_14.png" alt="" role="presentation" class="img-fluid atto_image_button_text-bottom" width="489" height="169"> Practice 8: Sketch the graph of <a target="_blank" href="https://learn.saylor.org/filter/tex/displaytex.php?texexp=y%20%3D%20INT%28%20x%5E2%20%29" id="action_link634cadbe05b7338" title="TeX"><img class="texrender" title="y = INT( x^2 )" alt="y = INT( x^2 )" src="https://learn.saylor.org/filter/tex/pix.php/b05f80691e42d2514360f5f89fdf527d.svg"></a><script type="math/tex">y = INT( x^2 ) for <a target="_blank" href="https://learn.saylor.org/filter/tex/displaytex.php?texexp=%E2%80%932%20%E2%89%A4%20x%20%E2%89%A4%202" id="action_link634cadbe05b7339" title="TeX"><img class="texrender" title="–2 ≤ x ≤ 2" alt="–2 ≤ x ≤ 2" src="https://learn.saylor.org/filter/tex/pix.php/0048225a1cfaed2ead7b046bbead42e5.svg"></a><script type="math/tex">–2 ≤ x ≤ 2

How do you find the greatest integer less than or equal?

The greatest integer less than or equal to a number x is represented as ⌊x⌋. We will round off the given number to the nearest integer that is less than or equal to the number itself. Mathematically, the greatest integer function ⌊x⌋ can be defined as follows: ⌊x⌋ = n, where n ≤ x < n + 1 and 'n' is an integer.

Which function returns the largest integer that is less than or equal to its argument?

The method floor gives the largest integer that is less than or equal to the argument.

What is the largest integer function?

The greatest integer function is a function that results in the integer nearer to the given real number. It is also called the step function. The greatest integer function rounds off the given number to the nearest integer.