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Functia nula, identica, constanta, modul, gradul I, II, rationala, radical, putere, exponentiala, logaritmica referat



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?. FUNCTII ELEMENTARE

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  1. f: A®|R, AÌ|R, "xIA f(x)=0 – functia nula;

  • graficul este un punct (originea axelor).

  1. 1A:A®A, "xIA 1A(x)=x – functia identica;



  • graficul este prima bisectoare. kj776b8579bjjo

  1. f: |R®|R, f(x)=a, aI|R - functia constanta;

  • graficul este o dreapta paralela cu axa OX.

  1. f: |R®|R, f(x)=|x |= - functia modul;

  • graficul este prima si a doua bisectoare.

  1. f: |R®|R, f(x)=ax+b, a, bI|R, a¹0 - functia de gradul intai;

  • graficul este o dreapta.

  1. f: |R®|R, f(x)=ax2+bx+c, a, b, cI|R, a¹0 - functia de gradul al doilea;

  • graficul este o parabola.

  1. f: |R-{x÷ Q(x)¹0}®|R, f(x)=, P(x), Q(x)I|R[x] polinoame - functia rationala;

  1. f: |R +®|R +, f(x)= sau f: |R ®|R, f(x)= - functia radical;

  1. f: (0, ¥)®(0, ¥), f(x)=x n, nI|R – functia putere;

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  1. f: |R®(0, ¥), f(x)=a x, a>0, a¹1, aI|R – functia exponentiala;

  1. f: (0, ¥)®|R, f(x)=logax , a>0, a¹1, aI|R – functia logaritmica;

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  1. f: |R®[-1, 1], f(x)=sin x (restrictia f: [-, ]®[-1, 1]) – functia sinus;

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  1. f: [-1, 1]® [-, ], f(x)=arcsin x – functia arcsinus;

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  58776bkd79bjo1q

  1. f: |R®[-1, 1], f(x)=cos x (restrictia f: [0,p]®[-1, 1]) – functia cosinus;

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  58776bkd79bjo1q

  1. f: [-1, 1]® [0, p], f(x)=arcosin x – functia arcosinus;

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  1. f: |R-{+kpú kIZ}®|R, f(x)=tg x (restrictia f: (-, )®|R) – functia tangenta;

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  1. f: |R® (-, ), f(x)=arctg x – functia arctangenta;

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  1. f: |R-{kpú kIZ}®|R, f(x)=ctg x (restrictia f: (0,p)®|R) – functia cotangenta;

  2. f: |R® (0, p), f(x)=arcctg x – functia arccotangenta;

  3. f:|R®{-1, 0, 1}, f(x)=sign(x)=- functia signum (semn);

  4. f:|R®{0, 1}, f(x)=- functia lui Heaviside (treapta unitate);

  5. f:|R®Z, f(x)=[x]= - functia parte intreaga;

  6. f:|R®[0, 1)Z, f(x)=x-[x] - functia parte zecimala;

  7. f:|R®|R, f(x)=sh x= - functia sinus hiperbolic;

  8. f:|R®|R, f(x)=ch x= - functia cosinus hiperbolic;

  9. f:|R®|R, f(x)=th x= - functia tangenta hiperbolica;

  10. f:|R®|R, f(x)=cth x= - functia cotangenta hiperbolica;