Asymptoty funkce

Project ID: 
6000000063
Accepted: 
Podoblast: 
Typ: 
Layout: 
Question: 
Přiřaďte grafům funkcí jejich předpisy. (Nápověda: Všímejte si asymptot grafů.)
Question 1: 
{\obrA}
Question 1 Image: 
Answer 1: 

$f(x)=\frac1{2x^2}-x$

Question 2: 
{\obrB}
Question 2 Image: 
Answer 2: 

$f(x)=\frac{x^2}{x-1}$

Question 3: 
{\obrC}
Question 3 Image: 
Answer 3: 

$f(x)=\frac{x^2}{1-x^2}$

Question 4: 
{\obrD}
Question 4 Image: 
Answer 4: 

$f(x)=\frac2x-\frac x2$

Question 5: 
{\obrE}
Question 5 Image: 
Answer 5: 

$f(x)=\frac{2x}{x^2+1}+1$

Question 6: 
{\obrF}
Question 6 Image: 
Answer 6: 

$f(x)=\frac{x^3}{(x-1)^2}$

Answer 7: 

$f(x)=\frac{x^3}{x^2-1}$

Answer 8: 

$f(x)=\frac{2x+1}{x^2}$

Tex: 
% tiket 32713 \NastavOD{4} \def\obrA{\obrMsr[x=0.7cm,y=0.5cm]{-4}{4}{-3}7 { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2} \obrPopisY[left]{-2,2,4,6} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-1,1,3,5} \obrFce[dashed,black,thin]{-(\x)} \obrFce[domain=-4:-0.25]{1/(2*(\x)^2)-(\x)} \obrFce[domain=0.25:4]{1/(2*(\x)^2)-(\x)} }} \def\obrB{\obrMsr[x=0.5cm,y=0.3cm]{-5}{5}{-8}{10} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,-2,2,4} \obrPopisY[left]{-6,-4,-2,2,4,6,8} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-7,-5,-3,-1,1,3,5,7,9} \obrFce[dashed,black,thin]{(\x)+1} \draw[dashed,black,thin] (1,-8) -- (1,10); \obrFce[domain=-5:0.99]{(\x)^2/((\x)-1)} \obrFce[domain=1.01:5]{(\x)^2/((\x)-1)} }} \def\obrC{\obrMsr[x=0.6cm,y=0.6cm]{-4}{4}{-4}{4} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2} \obrPopisY[left]{-2,2} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-3,-1,1,3} \obrFce[dashed,black,thin]{-1} \draw[dashed,black,thin] (-1,-4) -- (-1,4); \draw[dashed,black,thin] (1,-4) -- (1,4); \obrFce[domain=-4:-1.01]{(\x)^2/(1-(\x)^2)} \obrFce[domain=-0.99:0.99]{(\x)^2/(1-(\x)^2)} \obrFce[domain=1.01:4]{(\x)^2/(1-(\x)^2)} }} \def\obrD{\obrMsr[x=0.5cm,y=0.5cm]{-5}{5}{-5}{5} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,-2,2,4} \obrPopisY[left]{-4,-2,2,4} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-3,-1,1,3} \obrFce[dashed,black,thin]{-0.5*(\x)} \obrFce[domain=-5:-0.25]{2/(\x)-(\x)/2} \obrFce[domain=0.25:5]{2/(\x)-(\x)/2} }} \def\obrE{\obrMsr[x=0.5cm,y=0.9cm]{-6}{6}{-2}{3} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,-2,2,4} \obrPopisY[left]{2} \obrZnackyX{-5,-3,-1,1,3,5} \obrZnackyY{-1,1} \obrFce[dashed,black,thin]{1} \obrFce{2*(\x)/(1+(\x)^2)+1} }} \def\obrF{\obrMsr[x=0.5cm,y=0.3cm]{-5}{6}{-5}{12} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,-2,2,4} \obrPopisY[left]{-4,-2,2,4,6,8,10} \obrZnackyX{-3,-1,1,3,5} \obrZnackyY{-3,-1,1,3,5,7,9,11} \obrFce[dashed,black,thin]{(\x)+2} \draw[dashed,thin] (1,-5) -- (1,12); \obrFce[domain=-5:0.9]{(\x)^3/((\x)-1)^2} \obrFce[domain=1.25:6]{(\x)^3/((\x)-1)^2} }}