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\documentclass[a5paper]{handout}
\csname endofdump\endcsname
\geometry{left=1.2cm}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\pgfplotsset{vasymptote/.style={
before end axis/.append code={
\draw[densely dashed] ({rel axis cs:0,0} -| {axis cs:#1,0})
-- ({rel axis cs:0,1} -| {axis cs:#1,0});
}
}}
\pgfplotsset{hasymptote/.style={
before end axis/.append code={
\draw[densely dashed] ({rel axis cs:0,0} |- {axis cs:0,#1})
-- ({rel axis cs:1,0} |- {axis cs:0,#1});
}
}}
\pgfmathdeclarefunction{fFunc}{1}{\pgfmathparse{-0.2*(#1)+4}}
\pgfmathdeclarefunction{gFunc}{1}{\pgfmathparse{0.5*(#1)-1}}
\pgfmathdeclarefunction{hFunc}{1}{\pgfmathparse{1/(#1-1)+3}}
\title{Wiederholung Funktionen}
\setcounter{section}{42}
\begin{document}
\thispagestyle{empty}
\makedate
\begin{defbox}{Merke}
Eine Funktion beschreibt eine \pgap{\Large \boldgreen{eindeutige}~~~~} Zuordnung zwischen zwei \pgap{\huge Mengen~~~~}.
\end{defbox}
\vspace{-0.1cm}
\begin{tabular}{p{0.5\linewidth} p{0.5\linewidth}}
\vspace{-4cm}
Eine Funktion der Form \vspace{0.3cm}\newline
$\bm{f(x) =} \solution{\frac{\delta y}{\delta x}x +t}$ \vspace{0.3cm}\newline
$\bm{f:x} \mapsto \solution{mx +t}$ \vspace{0.3cm}\newline
heißt \boldgreen{lineare Funktion}. \vspace{0.4cm} \newline
$m :=$ \solution{Steigung} \vspace{0.2cm}\newline
$t :=$ \solution{Y-Achsenabschnitt} \newline
&%
\resizebox{\linewidth}{!}{
\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xtick={-6,...,3},
ytick={-1,...,5},
xlabel={$x$},
ylabel={$y$},
xlabel style={above right},
ylabel style={above right},
ymin=-2, ymax=5.5,
xmin=-6.2, xmax=4.2,
grid=both,
unbounded coords=discard
]
\addplot[domain=-7:4, samples=50, red, thick] (\x, {fFunc(\x)});
\addplot[domain=-3:4, samples=50, blue, thick] (\x, {gFunc(\x)});
\end{axis}
\node at (1, 4) {\textcolor{red}{$\bm{f(x) =}$}};
\node at (1, 1.9) {\textcolor{blue}{\bm{$g(x) =}$}};
\end{tikzpicture}
}
\faIcon{pencil-alt} Bestimme die Steigung und die Funktionsterme der Funktionen $f$ und $g$. \\
\end{tabular}
\begin{tabular}{c}
\begin{tabular}{p{0.5\linewidth} p{0.5\linewidth}}
\vspace{-4cm}
Eine Funktion der Form \vspace{0.3cm}\newline
$\bm{f:x \mapsto \frac{a}{x+b} + c}$ \solution{$(a, b, c \in \mathbb{R})$} \vspace{0.3cm}\newline
heißt \psolution{\boldgreen{gebrochen rationale Funktion}.} \vspace{0.4cm}\newline
$D = \mathbb{R} \setminus \{\solution{-b\text{~~}}\}$ \vspace{0.2cm}\newline
$a :=$ \solution{Streckung / Stauchung} \vspace{0.2cm}\newline
$b :=$ \solution{Verschiebung an X-Achse} \vspace{0.2cm}\newline
$c :=$ \solution{Verschiebung an Y-Achse} \vspace{0.2cm}\newline
&%
\resizebox{\linewidth}{!}{
\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xtick={-4,...,4},
ytick={-3,...,6},
xlabel={$x$},
ylabel={$y$},
xlabel style={above right},
ylabel style={above right},
ymin=-3.5, ymax=6.5,
xmin=-4.2, xmax=4.2,
grid=both,
unbounded coords=discard,
vasymptote=1,
hasymptote=3,
]
\addplot[domain=-4:0.9, samples=200, blue, thick] (\x, {hFunc(\x)});
\addplot[domain=1.1:4, samples=200, blue, thick] (\x, {hFunc(\x)});
\end{axis}
\node at (0.5, 2.85) {\textcolor{blue}{\bm{$g(x) =}$}};
\end{tikzpicture}
} \\
\end{tabular} \\[-0.75cm]
\begin{tabularx}{\linewidth}{X p{2cm}}
\vspace{-1.5cm}\faIcon{hands-helping} Scannt den QR-Code und untersucht, wie die Schieberegler $a$, $b$ und $c$ den Graph der Funktion $g$ verändern. &
\includegraphics[keepaspectratio, height=2cm]{img/geogebra_qrcode.png} \\
\end{tabularx}
\end{tabular}
\end{document}
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