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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク constant function ： ウィキペディア英語版 constant function In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function $y(x)\; =\; 4$ is a constant function because the value of  $y(x)$  is 4 regardless of the input value $x$ (see image). ==Basic properties== As a real-valued function of a real-valued argument, a constant function has the general form  $y(x)=c$  or just  $y=c$  . :Example: The function  $y(x)=2$  or just  $y=2$  is the specific constant function where the output value is  $c=2$. The domain of this function is the set of all real numbers ℝ. The codomain of this function is just . The independent variable ''x'' does not appear on the right side of the function expression and so its value is "vacuously substituted". Namely ''y''(0)=2, ''y''(−2.7)=2, ''y''(π)=2,.... No matter what value of ''x'' is input, the output is "2". :Real-world example: A store where every item is sold for the price of 1 euro. The graph of the constant function $y=c$ is a horizontal line in the plane that passes through the point $(0,c)$. In the context of a polynomial in one variable ''x'', the non-zero constant function is a polynomial of degree 0 and its general form is $f(x)\; =\; c\; \backslash ,\; ,\backslash ,\backslash ,\; c\; \backslash neq\; 0$ . This function has no intersection point with the ''x''-axis, that is, it has no root (zero). On the other hand, the polynomial  $f(x)=0$  is the identically zero function. It is the (trivial) constant function and every ''x'' is a root. Its graph is the ''x''-axis in the plane. A constant function is an even function, i.e. the graph of a constant function is symmetric with respect to the ''y''-axis. In the context where it is defined, the derivative of a function is a measure of the rate of change of function values with respect to change in input values. Because a constant function does not change, its derivative is 0. This is often written:  $(c)\text{'}=0$ . The converse is also true. Namely, if ''y'''(''x'')=0 for all real numbers ''x'', then ''y''(''x'') is a constant function.〔(【引用サイトリンク】title=Zero Derivative implies Constant Function )〕 :Example: Given the constant function   $y(x)=-\backslash sqrt$  . The derivative of ''y'' is the identically zero function   $y\text{'}(x)=(-\backslash sqrt)\text{'}=0$  . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「constant function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.