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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
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\@author% <------ Authors
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{\large \@date}%
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%opening
\newcommand{\snovdn}{Potenčna funkcija z naravnim eksponentom }
\newcommand{\predmdn}{mat}
\newcommand{\predmkaj}{domace\_naloge}
\newcommand{\stevilkadn}{32}
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\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}}
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\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{vaje2} 117 / 754 -- 760 (2 sodi, 2 lihi)
%\tableofcontents
\begin{enumerate}[label=\textbf{\arabic*.}] % 758, 754, 759, 755
\setcounter{enumi}{753}
\item Nariši grafe funkcij.
\begin{multicols}{4}
\begin{enumerate}[label=\textbf{\xslalph*)}]
\item $f(x)=x^3$
\item $g(x)=(x-1)^3$
\item $h(x)=x^3-1$
\item $m(x)=\frac{1}{2}x^3$
\end{enumerate}
\end{multicols}
\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, {x^3});
\addlegendentry{$f(x)=x^3$}
\addplot[black, densely dashed] (x, {(x-1)^3});
\addlegendentry{$g(x)=(x-1)^3$}
\addplot[black, densely dotted] (x, {x^3-1});
\addlegendentry{$h(x)=x^3-1$}
\addplot[black, densely dashdotdotted] (x, {(-1/2)*x^3)});
\addlegendentry{\raisebox{7pt}{$m(x) = -\frac{1}{2}x^3$}}
\end{axis}
\end{tikzpicture}
\newpage
\item Nariši grafe funkcij.
\begin{multicols}{4}
\begin{enumerate}[label=\textbf{\xslalph*)}]
\item $f(x)=-x^2$
\item $g(x)=2-x^2$
\item $h(x)=(x+1)^2+2$
\item $m(x)=|x^2-1|$
\end{enumerate}
\end{multicols}
\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, {-x^2});
\addlegendentry{$f(x)=-x^2$}
\addplot[black, densely dashed] (x, {2-x^2});
\addlegendentry{$g(x)=2-x^2$}
\addplot[black, densely dotted] (x, {(x+1)^2+2});
\addlegendentry{$h(x)=(x+1)^2+2$}
\addplot[black, densely dashdotdotted] (x, {abs(x^2-1)});
\addlegendentry{$m(x)=|x^2-1|$}
\end{axis}
\end{tikzpicture}
\setcounter{enumi}{757}
\newpage
\item Nariši graf funkcije $f(x)=\frac{1}{2}(x+2)^3-1$.
\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)^3-1});
\addlegendentry{\raisebox{7pt}{$f(x)=\frac{1}{2}(x+2)^3-1$}}
\end{axis}
\end{tikzpicture}
\newpage
\item Nariši grafe funkcij $f(x)=1-(x-1)^2$, $g(x)=|f(x)|$, $h(x)=f(|x|)$ in $k(x)=|f(|x|)|$.
\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-(x-1)^2});
\addlegendentry{$f(x)=1-(x-1)^2$}
\addplot[blue, densely dashed] (x, {abs(1-(x-1)^2)});
\addlegendentry{$g(x)=|f(x)|$}
\addplot[green, densely dashed] (x, {1-(abs(x)-1)^2});
\addlegendentry{$h(x)=f(|x|)$}
\addplot[red, densely dashdotdotted] (x, {abs(1-(abs(x)-1)^2)});
\addlegendentry{$k(x)=|f(|x|)|$}
\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}
