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Line 7: == Basic properties == [[Image:wiki constant function 175 200.png\|270px\|right\|Constant function ''y''(''x'') = 4\|thumb\|An example of a constant function is {{math\|1=''y''(''x'') = 4}}, because the value of {{math\|''y''(''x'')}} is 4 regardless of the input value {{mvar\|x}}.]] As a real-valued function of a real-valued argument, a constant function has the general form {{math\|1=''y''(''x'') = ''c''}} or just {{nowrap\|{{math\|1=''y'' = ''c''}}.}} For example, the function {{math\|1=''y''(''x'') = 4}} is the specific constant function where the output value is {{math\|1=''c'' = 4}}. The [[___domain of a function\|___domain of this function]] is the set of all [[real number]]s. The [[Image (mathematics)\|image]] of this function is the [[Singleton (mathematics)\|singleton]] set {{math\|{{mset\|4}}}}. The independent variable {{nowrap\|1=''x''}} does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely {{math\|1=''y''(0) = 24}}, {{math\|1=''y''(−2.7) = 24}}, {{math\|1=''y''(π) = 24}}, and so on. No matter what value of {{math\|''x''}} is input, the output is {{math\|4}}.<ref>{{cite book \| last = Tanton \| first = James \| year = 2005

Constant function: Difference between revisions