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SerloDie freie Lernplattform

Bestimme die Asymptoten:

  1. f(x)=1xf(x)=\frac1x

  2. f(x)=11xf\left(x\right)=1-\frac1x

  3. f(x)=1+xxf\left(x\right)=\frac{1+x}x

  4. f(x)=x1+xf(x)=\frac x{1+x}

  5. f(x)=x21+x2f(x)=\frac{x^2}{1+x^2}

  6. f(x)=x1+xf(x)=\frac{\left|x\right|}{1+x}

  7. f(x)=1+1xf(x)=1+\frac1x

  8. f(x)=x+1xf(x)=x+\frac1x

  9. f(x)=x1xf(x)=x-\frac1x

  10. f(x)=x2+1xf(x)=x^2+\frac1x

  11. f(x)=x+1x2f(x)=x+\frac1{x^2}

  12. f(x)=3x3x22x+2f\left(x\right)=\dfrac{3x-3}{x^2-2x+2}

  13. f(x)=x21x22x+1f\left(x\right)=\frac{x^2-1}{x^2-2x+1}

  14. f(x)=2x3x2x3+x2f(x)=\frac{2x^3-x^2}{x^3+x^2}

  15. f(x)=x+xx1f(x)=\frac{x+\left|x\right|}{\left|x\right|-1}

  16. f(x)=4x3+8x2+23x9x218x+9f(x)=\frac{-4x^3+8x^2+23x}{9x^2-18x+9}

  17. f(x)=(x+3)2(x21)(x+3)(x2+1)f(x)=\frac{\left(x+3\right)^2\cdot(x^2-1)}{\left(x+3\right)\cdot(x^2+1)}