functia putere
DESCRIPTION
Liceul Pedagogic "N.Bolcas", Beius. Functia putere. Realizat de: Hus Alin Takacs Bianca Laza Bianca Ganea Alina Martin Madalina Balint Adrian Petrut Bogdan Petrut Rares. Coordonator: Lezeu Eugenia. - PowerPoint PPT PresentationTRANSCRIPT
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Definiţie: Funcţia f: R → R, f(x)=x
cu n є N* se numeşte funcţie putere cu exponent număr natural.
Pentru n=1 si n=2 se obţin funcţiile putere de gradul I şi gradul II.
f : ℝ → ℝ , f(x)= x, respectiv f : ℝ→ ℝ , f(x)= x²
n
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Funcţia putere de gradul I f(x)= x este funcţie impară, strict
crescătoare pe ℝ şi bijectivă.
Funcţia putere de gradul II
f(x)= x² este funcţie pară,
strict descrescătoare pe (-∞,0], strict crescătoare pe [0, ∞), nu
este injectiva sau surjectivă.
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Principalele atribute ce caracterizează această funcţie:
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Fie n є ℕ* si
f : ℝ→ ℝ , f(x)= xⁿ atunci :
a) funcţia f este pară pentru n-numar par şi impară pentru n-impar.
b) pentru n-numar impar funcţia f este strict crescătoare.
c) pentru n-numar par funcţia f este
strict descrescătoare pe (-∞,0], strict crescătoare pe [0, ∞).
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monotonia:
paritate:
semn:
f(x)=xn, f:RR, nN*
R pe ecrescatoarstrict f(x) impar n
) [0, pe ecrescatoarstrict f(x) par n
0] ,(- pe oaredescrescatstrict f(x) par n
origine de fata simetric graficul impara, f(x) impar n
OY de fata simetric graficul para, f(x) par n
0)(impar ,0
0)(par ,0
0)(2nN,n 0,
xfnx
xfnx
xfx
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Definitie:f =x
f:R-{0}R, nN*
monotonia:
paritatea:
semn:
{0}-R pe oaredescrescatstrict f(x) impar n
) (0, pe oaredescrescatstrict f(x) par n
0) ,(- pe ecrescatoarstrict f(x) par n
origine de fata simetric graficul impara, f(x) impar n
OY de fata simetric graficul para, f(x) par n
0)(impar ,0
0)(par ,0
0)(1nN,n 0,
xfnx
xfnx
xfx
-n(x)
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Pentru α =0, se obţine funcţia constantă f :(0, + ∞)→ ℝ, f(x) =1.
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Bibliografie:-Manual de matematica pt cls. a Xa , Mircea Ganga , Editura Mathpress, 2005
http://www.preferatele.com/docs/matematica/2/puteri-si-radicali-16.php
http://www.ecursuri.ro/referate/referate.php?report=puteri-si-radicali
http://www.scritube.com/stiinta/matematica/PUTERI-I-RADICALI321815224.php
http://meditatiionline.ro/44100-24-283-0-0-Formule_Matematica_Functii_Puteri_cu_exponent_real.html