What is Constant function?
[[Image:wiki_constant_function_175_200.png|thumb|right|Constant function ''y''=4]] In [[mathematics]], a '''constant function''' is a [[function (mathematics)|function]] whose output value is the same for every input value.<ref>{{cite book|title=Encyclopedia of Mathematics|url=https://archive.org/details/encyclopediamath00tant_807|last1=Tanton|first1=James|year=2005|publisher=Facts on File, New York|isbn=0-8160-5124-0|page=[https://archive.org/details/encyclopediamath00tant_807/page/n102 94]}} {{in lang|en}}</ref><ref>{{cite web | url=http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf |title=Oxford Concise Dictionary of Mathematics, Constant Function | author=C.Clapham, J.Nicholson | publisher =Addison-Wesley | year =2009|page=175|language=en|access-date=1 January 2014}}</ref><ref>{{cite book|title=CRC Concise Encyclopedia of Mathematics|url=https://archive.org/details/crcconciseencycl0000weis|last1=Weisstein|first1=Eric|publisher=CRC Press, London|isbn=0-8493-9640-9|year=1999|page=[https://archive.org/details/crcconciseencycl0000weis/page/313 313]}} {{in lang|en}}</ref> For example, the function <math>y(x) = 4</math> is a constant function because the value of &nbsp;<math>y(x)</math> &nbsp;is 4 regardless of the input value <math>x</math> (see image). ==Basic properties== Formally, a constant function ''f''(''x''):'''R'''→'''R''' has the form &nbsp;<math>f(x)=c</math>. Usually we write <math>y(x)=c</math> &nbsp;or just &nbsp;<math>y=c</math>. *The function ''y''=''c'' has 2 [[variable]]s ''x'' and ''у'' and 1 [[constant]] ''c''. (In this form of the function, we do not see ''x'', but it is there.) **The constant ''c'' is a real number. Before working with a linear function, we replace ''c'' with an actual number. **The [[function (mathematics)|domain]] or input of ''y''=''c'' is '''R'''. So any real number ''x'' can be ''input''. However, the output is always the value ''c''. **The [[function (mathematics)|range]] of ''y''=''c'' is also '''R'''. However, because the output is always the val