Project ID:
6000000046
Accepted:
Type:
Layout:
Question:
Use the given graphs to find domains of corresponding functions and match each function with its domain.
Questions Title:
Graphs:
Answers Title:
Domains:
Question 1:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=3\mathrm{e}^{-x^2}-1$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrA}
\end{minipage}
Answer 1:
$\mathbb{R}$
Question 2:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=\left\{\begin{array}{ll}-0.5(x+4)^2+4\text{, } & x\leq -2 \\ & \\ 0.5(x-4)^2-4\text{, } & x\geq 2\end{array}\right.$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrB}
\end{minipage}
Answer 2:
$(-\infty;-2]\cup[2;\infty)$
Question 3:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=\left\{\begin{array}{ll}-\frac8{x+2}+2\text{, } & x < -2 \\ & \\ \frac8{x-2}+2\text{, } & x > 2 \end{array}\right.$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrC}
\end{minipage}
Answer 3:
$(-\infty;-2)\cup(2;\infty)$
Question 4:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=\left\{\begin{array}{ll} -\frac8x+2\text{, } & x < 0 \\ & \\ -\frac8{x}-2\text{, } & x >0\end{array}\right.$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrD}
\end{minipage}
Answer 4:
$\mathbb{R}\setminus\{0\}$
Question 5:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=\left\{\begin{array}{ll} \log_2(x+2)+1\text{, } & -2 < x < 0 \\ & \\ \log_2(-x+2)+1\text{, } & 0 \leq x < 2\end{array}\right.$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrE}
\end{minipage}
Answer 5:
$(-2;2)$
Question 6:
\begin{minipage}{0.5\linewidth}
\vfill
\centering
$f(x)=2\text{, }\ x > 0$
\vfill
\end{minipage}
\begin{minipage}{0.4\linewidth}
{\obrF}
\end{minipage}
Answer 6:
$(0;\infty)$
Tex:
% ticket 32699
\NastavOD{3}
\def\obrA{\obrMsr[x=0.6cm,y=0.6cm]{-4}{4}{-4}4
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-4,-4) grid (4,4);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2}
\obrPopisY[left]{-2,2}
\obrFce{3*exp(-(\x)^2)-1}
\draw[dashed] (-4,-1) -- (4,-1);
}}
\def\obrB{\obrMsr[x=0.2cm,y=0.2cm]{-12}{12}{-12}{12}
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-12,-12) grid (12,12);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-8,-4,4,10}
\obrPopisY[left]{-8,-4,4,8}
\obrFce[domain=-10:-2]{-0.5*(\x+4)^2+4}
\obrFce[domain=10:2]{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]{-12}{12}{-4}{20}
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-12,-4) grid (12,20);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-8,-4,4,10}
\obrPopisY[left]{4,8,12,16}
\obrFce[domain=-12:-2.25]{-8/(\x+2)+2}
\obrFce[domain=12:2.25]{8/(\x-2)+2}
\draw[dashed] (-12,1) -- (12,1);
\draw[dashed] (-2,-4) -- (-2,20);
\draw[dashed] (2,-4) -- (2,20);
}}
\def\obrD{\obrMsr[x=0.2cm,y=0.2cm]{-12}{12}{-12}{12}
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-12,-12) grid (12,12);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-8,-4,4,10}
\obrPopisY[left]{-8,-4,4,8}
\obrFce[domain=-12:-0.25]{-8/(\x)+2}
\obrFce[domain=12:0.25]{-8/(\x)-2}
\draw[dashed] (-12,2) -- (12,2);
\draw[dashed] (-12,-2) -- (12,-2);
}}
\def\obrE{\obrMsr[x=0.6cm,y=0.6cm]{-4}{4}{-6}{4}
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-4,-6) grid (4,4);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2}
\obrPopisY[left]{-4,-2,2}
\obrFce[domain=-1.995:0]{ln(\x+2)/ln(2)+1}
\obrFce[domain=1.995:0]{ln(-\x+2)/ln(2)+1}
\draw[dashed] (-2,-6) -- (-2,4);
\draw[dashed] (2,-6) -- (2,4);
}}
\def\obrF{\obrMsr[x=0.6cm,y=0.6cm]{-2}{6}{-4}{4}
{
\footnotesize
\obrClip
\draw[gray!20,thin, step=1] (-4,-4) grid (6,4);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{2,4}
\obrPopisY[left]{-2,2}
\obrFce[domain=0:6]{2}
\draw[thick,red,fill=white] (0,2) circle (2pt);
}}