Obor hodnôt funkcie z grafu

Project ID: 
6000000058
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Question: 
Priraďte dané grafy funkcií k ich oborom hodnôt. (Prerušované čiary predstavujú asymptoty daných funkcií.)
Questions Title: 
Grafy:
Answers Title: 
Obory hodnôt:
Question 1: 
\begin{minipage}{0.5\linewidth} \kern -5em $f_1(x)=3\mathrm{e}^{-x^2}-1$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrA} \end{minipage}
Answer 1: 

$(-1;2\rangle$

Question 2: 
\begin{minipage}{0.5\linewidth} \kern -10em $f_2(x)=\left\{\begin{array}{ll} -0{,}5(x+4)^2+4; & x\in(-\infty;-2\rangle \\ \\ 0{,}5(x-4)^2-4; & x\in\langle-2;\infty)\end{array} \right.$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrB} \end{minipage}
Answer 2: 

$\mathbb{R}$

Question 3: 
\begin{minipage}{0.5\linewidth} \kern -10em $f_3(x)=\left\{\begin{array}{ll} -\frac8{x+2}+2; & x\in(-\infty;-2) \\ \\ \frac8{x-2}+2; & x\in(2;\infty)\end{array} \right.$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrC} \end{minipage}
Answer 3: 

$(2;\infty)$

Question 4: 
\begin{minipage}{0.5\linewidth} \kern -10em $f_4(x)=\left\{\begin{array}{ll} -\frac8{x}+2; & x\in(-\infty;0) \\ \\ -\frac8{x}-2; & x\in(0;\infty)\end{array} \right.$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrD} \end{minipage}
Answer 4: 

$(-\infty;-2)\cup(2;\infty)$

Question 5: 
\begin{minipage}{0.5\linewidth} \kern -10em $f_5(x)=\left\{\begin{array}{ll} \log_2(x+2)+1; & x\in(-2;0) \\ \\ \log_2(-x+2)+1; & x\in\langle0;2)\end{array} \right.$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrE} \end{minipage}
Answer 5: 

$(-\infty;2\rangle$

Question 6: 
\begin{minipage}{0.5\linewidth} \kern -10em $f_6(x)=2;\ x\in(0;\infty)$ \end{minipage} \hfill \begin{minipage}{0.5\linewidth} {\obrF} \end{minipage}
Answer 6: 

$\{2\}$

Tex: 
%tiket 32698 \NastavOD{3} \def\obrA{\obrMsr[x=0.6cm,y=0.6cm,]{-4}4{-3}4 { \footnotesize \obrClip \draw[gray!30,thin,step=1] (-4,-3) grid (4,4); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-2,2} \obrPopisY[left]{-2,2} \obrZnackyX{-3,-1,1,3} \obrZnackyY{-1,1,3} \draw[dashed] (-4,-1) -- (4,-1); \obrFce{3*exp(-(\x)^2)-1} }} \def\obrB{\obrMsr[x=0.2cm,y=0.2cm,]{-14}{14}{-12}{12} { \footnotesize \obrClip \draw[gray!30,thin,step=2] (-14,-12) grid (14,12); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-12,-8,-4,4,8,12} \obrPopisY[left]{-8,-4,4,8} \obrZnackyX{-10,-6,-2,2,6,10} \obrZnackyY{-10,-6,-2,2,6,10} \obrFce[domain=-14:-2]{-0.5*((\x)+4)^2+4} \obrFce[domain=2:14]{0.5*((\x)-4)^2-4} \fill[red] (-2,2) circle (2pt); \fill[red] (2,-2) circle (2pt); }} \def\obrC{\obrMsr[x=0.2cm,y=0.2cm,]{-14}{14}{-4}{20} { \footnotesize \obrClip \draw[gray!30,thin,step=2] (-14,-4) grid (14,20); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-12,-8,-4,4,8,12} \obrPopisY[left]{4,8,12,16} \obrZnackyX{-10,-6,-2,2,6,10} \obrZnackyY{-2,2,6,10,14,18} \obrFce[domain=-14:-2.1]{-8/((\x)+2)+2} \obrFce[domain=2.1:14]{8/((\x)-2)+2} \draw[dashed] (-14,2) -- (14,2); \draw[dashed] (-2,-4) -- (-2,20); \draw[dashed] (2,-4) -- (2,20); }} \def\obrD{\obrMsr[x=0.2cm,y=0.2cm,]{-14}{14}{-10}{14} { \footnotesize \obrClip \draw[gray!30,thin,step=2] (-14,-10) grid (14,14); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-12,-8,-4,4,8,12} \obrPopisY[left]{-8,-4,4,8,12} \obrZnackyX{-10,-6,-2,2,6,10} \obrZnackyY{-6,-2,2,6,10} \obrFce[domain=-14:-0.1]{-8/(\x)+2} \obrFce[domain=0.1:14]{-8/(\x)-2} \draw[dashed] (-14,2) -- (14,2); \draw[dashed] (-14,-2) -- (14,-2); }} \def\obrE{\obrMsr[x=0.4cm,y=0.4cm,]{-6}{6}{-6}{6} { \footnotesize \obrClip \draw[gray!30,thin,step=2] (-6,-6) grid (6,6); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-4,4} \obrPopisY[left]{-4,4} \obrZnackyX{-2,2} \obrZnackyY{-2,2} \obrFce[domain=-1.999:0]{ln((\x)+2)/ln(2)+1} \obrFce[domain=0:1.999]{ln(-(\x)+2)/ln(2)+1} \draw[dashed] (-2,-6) -- (-2,6); \draw[dashed] (2,-6) -- (2,6); }} \def\obrF{\obrMsr[x=0.4cm,y=0.4cm,]{-4}{8}{-6}{6} { \footnotesize \obrClip \draw[gray!30,thin,step=2] (-4,-6) grid (8,6); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{4} \obrPopisY[left]{-4,4} \obrZnackyX{-2,2,6} \obrZnackyY{-2,2} \draw[red,thick] (0,2) -- (8,2); \draw[thick,draw=red,fill=white] (0,2) circle (2pt); }}