@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr: a skos:ConceptScheme . psr:-VQ2RSR5H-C skos:prefLabel "fonction carré"@fr, "square function"@en ; a skos:Concept ; skos:broader psr:-KF6VNW4H-5 . psr:-FF99PJ0L-W skos:prefLabel "algebraic function"@en, "fonction algébrique"@fr ; a skos:Concept ; skos:narrower psr:-KF6VNW4H-5 . psr:-KF6VNW4H-5 skos:definition """Real functions of the form

{\\\\displaystyle f(x)=cx^{n}}

, where

{\\\\displaystyle c\\ eq 0}

, are sometimes called power functions. When

{\\\\displaystyle n}

is an integer and

{\\\\displaystyle n\\\\geq 1}

, two primary families exist: for

{\\\\displaystyle n}

even, and for

{\\\\displaystyle n}

odd. In general for

{\\\\displaystyle c>0}

, when

{\\\\displaystyle n}

is even

{\\\\displaystyle f(x)=cx^{n}}

will tend towards positive infinity with increasing

{\\\\displaystyle x}

, and also towards positive infinity with decreasing

{\\\\displaystyle x}

. All graphs from the family of even power functions have the general shape of

{\\\\displaystyle y=cx^{2}}

, flattening more in the middle as

{\\\\displaystyle n}

increases. Functions with this kind of symmetry (

{\\\\displaystyle f(-x)=f(x)}

) are called even functions. When

{\\\\displaystyle n}

is odd,

{\\\\displaystyle f(x)}

's asymptotic behavior reverses from positive

{\\\\displaystyle x}

to negative

{\\\\displaystyle x}

. For

{\\\\displaystyle c>0}

{\\\\displaystyle f(x)=cx^{n}}

will also tend towards positive infinity with increasing

{\\\\displaystyle x}

, but towards negative infinity with decreasing

{\\\\displaystyle x}

. All graphs from the family of odd power functions have the general shape of

{\\\\displaystyle y=cx^{3}}

, flattening more in the middle as

{\\\\displaystyle n}

increases and losing all flatness there in the straight line for

{\\\\displaystyle n=1}

. Functions with this kind of symmetry (

{\\\\displaystyle f(-x)=-f(x)}

) are called odd functions. For

{\\\\displaystyle c<0}

, the opposite asymptotic behavior is true in each case
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Exponentiation#Power_functions)"""@en, """En mathématiques, et plus spécialement en analyse, les fonctions puissances sont les fonctions

f a

définies par

{\\\\displaystyle f_{a}:x\\\\mapsto x^{a}}

où

a

peut désigner un entier naturel, un entier relatif, un réel voire un complexe que l'on appelle l'exposant de la fonction puissance. Selon la nature de

a

, l'ensemble de définition de la fonction

f a

peut changer. Définie en général comme fonction de la variable réelle, on peut la trouver dans certains cas comme fonction complexe. Les fonctions puissances à exposant entier servent de base dans la construction des fonctions polynomiales et dans les développements en séries. Les fonctions puissances à exposant réel servent à modéliser des relations tant en physique qu'en biologie ou en économie.
(Wikipedia, L'Encylopédie Libre, https://fr.wikipedia.org/wiki/Fonction_puissance)"""@fr ; a skos:Concept ; skos:exactMatch , ; skos:narrower psr:-VQ2RSR5H-C ; dc:modified "2024-10-18"^^xsd:date ; skos:inScheme psr: ; skos:prefLabel "power function"@en, "fonction puissance"@fr ; skos:broader psr:-FF99PJ0L-W .