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% !TeX encoding = UTF-8
% !TeX spellcheck = sl_SI
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% \usepackage{multienum} % weird with labels
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% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
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{\LARGE \@title \par}%
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{\large
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\@author% <------ Authors
\end{tabular}\par}% <------
\vskip 1em%
{\large \@date}%
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\par
\vskip 1.5em}
%opening
\newcommand{\snovdn}{Transformacije na ravnini }
\newcommand{\predmdn}{mat}
\newcommand{\predmkaj}{domace\_naloge}
\newcommand{\stevilkadn}{31}
\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
\makeatletter
\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
\newcommand{\@xslalph}[1]{%
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\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
\or t\or u\or v\or z\or \v{z}
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}
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\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
\newcommand\vektor{\overrightarrow}
\newcommand{\iic}{I\textsuperscript{2}C }
\title{%
\snovdn --- \stevilkadn. domača naloga
\\
\large Matematika, Gimnazija Bežigrad}
\author{\begin{tabular}{rl}
\textbf{Profesor:} & prof. Vilko Domajnko \\
\textbf{Avtor:} & Anton Luka Šijanec, 2. a
% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
\end{tabular}}
\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}%
\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
\everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
\begin{document}
\maketitle
\begin{abstract}
Ta dokument vsebuje navodila in rešitve domače naloge snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam.
\end{abstract}
\paragraph{Navodilo naloge} \textbf{Mat3} (Mat2 verjetno): 114 / 1, 2, 3
%\tableofcontents
\begin{enumerate}[label=\textbf{\arabic*.}]
\item Prezrcali graf funkcije $f\left(x\right)=-\frac{1}{2}x+2$
\begin{tasks}[label=\textbf{\xslalph*)}](2)
\task čez abscisno os,
\task čez ordinatno os,
\task čez koordinatno izhodišče,
\task čez simetralo lihih kvadrantov
\end{tasks}
\begin{tikzpicture}
\begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
\addplot[black, solid] (x, {(-1/2)*x+2}) node[above,pos=.6] {$f$};
\addplot[black, densely dotted] (x, {-1*((-1/2)*x+2)}) node[above,pos=.6] {$a$};
\addplot[black, densely dashed] (x, {(1/2)*x+2}) node[above,pos=.6] {$b$};
\addplot[red, solid] (x, {(-1/2)*x-2}) node[above,pos=.6] {$c$};
\addplot[red, densely dotted] (x, {(-2)*x+4}) node[above,pos=.6] {$č$};
\addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x+2$}}
\addlegendentry{$a(x) = f\left(x\right)\cdot-1$}
\addlegendentry{\raisebox{7pt}{$b(x) = \frac{1}{2}x+2$}}
\addlegendentry{\raisebox{7pt}{$c(x) = -\frac{1}{2}x-2$}}
\addlegendentry{\raisebox{7pt}{$č(x) = -2x+4$}}
\end{axis}
\end{tikzpicture}
\newpage
\item Nariši grafa funkcij.
\begin{tasks}[label=\textbf{\xslalph*)}](2)
\task $f\left(x\right)=-\frac{1}{2}x+1$ in $g\left(x\right)=-2f\left(x\right)$
\task \color{red} $f\left(x\right)=-2x+1$ in $g\left(x\right)=f\left(3x\right)$ \color{black}
\task \color{green} $f\left(x\right)=\frac{1}{2}x-1$ in $g\left(x\right)=f\left(\frac{1}{2}x\right)$ \color{black}
\task \color{blue} $f\left(x\right)=-\frac{1}{2}x-3$ in $g\left(x\right)=\frac{1}{2}f\left(x\right)$ \color{black}
\end{tasks}
\begin{tikzpicture}
\begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
\addplot[black, solid] (x, {(-1/2)*x+1});
\addplot[black, densely dashed] (x, {-2*((-1/2)*x+1)});
\addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x+1$}}
\addlegendentry{$g(x) = -2f\left(x\right)$}
\addplot[red, solid] (x, {-2*x+1});
\addplot[red, densely dashed] (x, {-2*3*x+1});
\addlegendentry{$f(x) = -2x+1$}
\addlegendentry{$g(x) = f(3x)$}
\addplot[green, solid] (x, {(1/2)*x-1});
\addplot[green, densely dashed] (x, {(1/2)*(1/2)*x-1});
\addlegendentry{\raisebox{7pt}{$f(x) = \frac{1}{2}x-1$}}
\addlegendentry{\raisebox{7pt}{$g(x) = f\left(\frac{1}{2}x\right)$}}
\addplot[blue, solid] (x, {(-1/2)*x-3});
\addplot[blue, densely dashed] (x, {(1/2)*((-1/2)*x-3)});
\addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x-3$}}
\addlegendentry{\raisebox{7pt}{$g(x) = \frac{1}{2}f(x)$}}
\end{axis}
\end{tikzpicture}
\newpage
\item Nariši grafa funkcij.
\begin{tasks}[label=\textbf{\xslalph*)}](2)
\task $f\left(x\right)=-3x+1$ in $g\left(x\right)=f\left(x-3\right)$
\task \color{red} $f\left(x\right)=4x+3$ in $g\left(x\right)=f\left(x+1\right)$ \color{black}
\task \color{green} $f\left(x\right)=3x-1$ in $g\left(x\right)=f\left(x-1\right)-3$ \color{black}
\task \color{blue} $f\left(x\right)=-4x-1$ in $g\left(x\right)=f\left(x+2\right)-3$ \color{black}
\end{tasks}
\begin{tikzpicture}
\begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
\addplot[black, solid] (x, {-3*x+1});
\addplot[black, densely dashed] (x, {-3*(x-3)+1});
\addlegendentry{$f(x) = -3x+1$}
\addlegendentry{$g(x) = f(x-3)$}
\addplot[red, solid] (x, {4*x+3});
\addplot[red, densely dashed] (x, {4*(x+1)+3});
\addlegendentry{$f(x) = 4x+3$}
\addlegendentry{$g(x) = f(x+1)$}
\addplot[green, solid] (x, {3*x-1});
\addplot[green, densely dashed] (x, {(3*(x-1)-1)-3});
\addlegendentry{$f(x) = 3x-1$}
\addlegendentry{$g(x) = f(x-1)-3$}
\addplot[blue, solid] (x, {-4*x-1});
\addplot[blue, densely dashed] (x, {(-4*(x+2)-1)-3});
\addlegendentry{$f(x) = -4x-1$}
\addlegendentry{$g(x) = f(x+2)-3$}
\end{axis}
\end{tikzpicture}
\end{enumerate}
\section{Zaključek}
Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2021} ali \texttt{TeXLive 2020}.}
izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi
\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
\if\razhroscevanje1
\vfill
\section*{Razhroščevalne informacije}
Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
Grafi imajo natančnost \functionSamples\space točk na graf.
Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
Dokument se je generiral R0qK1KR2 \SI{}{\second}.
\fi
% \item $$$$ aaasecgeninsaaa R0qK1KR2
\end{document}
|
