Project ID:
6000000058
Accepted:
Tipo:
Layout:
Question:
Utiliza las gráficas dadas para determinar el rango de las funciones correspondientes. Empareja todas las funciones dadas con su rango. (Las lineas discontinuas representan asíntotas de funciones.)
Questions Title:
Gráficas:
Answers Title:
Rangos:
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:
$(-1;2]$
Question 2:
\begin{minipage}{0.5\linewidth}
\kern -5em
$f_2(x)=\left\{\begin{array}{ll} -0.5(x+4)^2+4; & x\in(-\infty;-2] \\ \\ 0.5(x-4)^2-4; & x\in[-2;\infty)\end{array} \right.$
\end{minipage}
\hfill
\begin{minipage}{0.5\linewidth}
{\obrB}
\end{minipage}
Answer 2:
$\mathbb{R}$
Question 3:
\begin{minipage}{0.5\linewidth}
\kern -5em
$f_3(x)=\left\{\begin{array}{ll} -\frac8{x+2}+2; & x\in(-\infty;-2) \\ \\ \frac8{x-2}+2; & x\in(2;\infty)\end{array} \right.$
\end{minipage}
\hfill
\begin{minipage}{0.5\linewidth}
{\obrC}
\end{minipage}
Answer 3:
$(2;\infty)$
Question 4:
\begin{minipage}{0.5\linewidth}
\kern -5em
$f_4(x)=\left\{\begin{array}{ll} -\frac8{x}+2; & x\in(-\infty;0) \\ \\ -\frac8{x}-2; & x\in(0;\infty)\end{array} \right.$
\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 -5em
$ f_5(x)=\left\{\begin{array}{ll} \log_2(x+2)+1; & x\in(-2;0) \\ \\ \log_2(-x+2)+1; & x\in[0;2)\end{array} \right.$
\end{minipage}
\hfill
\begin{minipage}{0.5\linewidth}
{\obrE}
\end{minipage}
Answer 5:
$(-\infty;2]$
Question 6:
\begin{minipage}{0.5\linewidth}
\kern -5em
$f_6(x)=2;\ x\in(0;\infty)$
\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);
}}