what is the greatest integer function
Video What is the Largest Integer Function The Largest Integer Function The Largest Integer Function is also known as a step function. The largest integer function rounds a number to the nearest integer less than or equal to the given number. The largest integer function has a step curve, which we will explore in the following sections. The domain of the largest integer function is (mathbb {R}) and its range is (mathbb {Z}). Therefore, the largest integer function simply rounds to the largest integer less than or equal to the given number. Here we will learn more about the largest integer function, its graph and properties. Read: What is the largest integer function 1. What is the largest integer function? 2. Largest integer function graph 3. Largest integer function properties 4. Largest integer function examples 5. Largest integer function practice questions 6. Frequently asked questions (FAQ) Functions largest integer is a function for the largest integer less than or equal to a number. The largest integer less than or equal to some x is represented as ⌊x⌋. We will round the given number to the nearest integer less than or equal to the number itself. Obviously, the input variable x can take on any real value. However, the output will always be an integer. Also, all integers will appear in the output set Read more: What is the si unit of temperature, the domain of this function is real numbers ((mathbb {R})), while its range will be integer ((mathbb {Z })). Look at the following examples of the largest integer function in the following table: Value of xf(x) = ⌊x⌋ 3.1 f (3.1) = ⌊3.1⌋ = 3 2,999 f (2,999) = ⌊2.999⌋ = 2 − 2.7 f (−2.7) = − 2.7⌋ = −3 −√2 f (−√2) = − √2⌋ = −2 4 f (4) = 4⌋ = 4 −7 f (−7) = ⌊ −7⌋ = −7 The graph of the largest integer function is called a degree curve because of its order structure. Let us graph the largest integer function. First, consider f(x) = ⌊x⌋, if x is an integer then the value of f will be x itself. If x is not an integer, then the value of x will be the integer immediately preceding x. For example:
- For all numbers in the range[01)thevalueoffwillbe0[01)thevalueoffwillbe0[01)giátrịcủafsẽbằng0[01)thevalueoffwillbe0
- Over the entire interval[12)fwilltakethevalue1[12)fwilltakethevalue1[12)fsẽnhậngiátrị1[12)fwilltakethevalue1
- In the interval[−10)fwilltakethevalue−1vv[−10)fwilltakethevalue−1andsoon[−10)fsẽnhậngiátrị−1vv[−10)fwilltakethevalue−1andsoon
Đọc thêm: Phạm vi của chuyến đi polaris com và đi theo nhóm Vì vậy, đối với một số nguyên n,[nn+1)sẽcógiátrịcủahàmsốnguyênlớnnhấtlànHàmcógiátrịkhôngđổigiữahaisốnguyênbấtkỳNgaysaukhisốnguyêntiếptheođếngiátrịhàmsẽnhảylênmộtđơnvịĐiềunàycónghĩalàgiátrịcủaftạix=1là1(chứkhôngphải0)dođósẽcó[nn+1)willhavethevalueofthegreatestintegerfunctionasnThefunctionhasaconstantvaluebetweenanytwointegersAssoonasthenextintegercomesthefunctionvaluejumpsbyoneunitThismeansthatthevalueoffatx=1is1(andnot0)hencetherewillbea[nn+1)sẽcógiátrịcủahàmsốnguyênlớnnhấtlànHàmcógiátrịkhôngđổigiữahaisốnguyênbấtkỳNgaysaukhisốnguyêntiếptheođếngiátrịhàmsẽnhảylênmộtđơnvịĐiềunàycónghĩalàgiátrịcủaftạix=1là1(chứkhôngphải0)dođósẽcó[nn+1)willhavethevalueofthegreatestintegerfunctionasnThefunctionhasaconstantvaluebetweenanytwointegersAssoonasthenextintegercomesthefunctionvaluejumpsbyoneunitThismeansthatthevalueoffatx=1is1(andnot0)hencetherewillbeaempty dot at (1,0) and a solid dot at (1,1) where the empty dot means excluding the value and the solid dot represents including the value. These observations lead us to the following graph.
The domain and range of the largest integer function
From the graph above, we can clearly see that the input to the function can be any real number but the output will always be an integer. Therefore, the domain of this function will be real numbers ((mathbb {R})), while its range will be integers ((mathbb {Z})). There are various properties related to the largest integral function. Some useful properties of the largest integer function are listed below.Read more: Tan 0 Degree | Top Q&A
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