1 files changed, 108 insertions, 10 deletions
diff --git a/Mathe/9/1/FunktionsWdh/handout.tex b/Mathe/9/1/FunktionsWdh/handout.tex
index 63bd997d..8fb3f1e7 100644
--- a/Mathe/9/1/FunktionsWdh/handout.tex
+++ b/Mathe/9/1/FunktionsWdh/handout.tex
@@ -1,15 +1,113 @@
-\documentclass[]{handout}
-\usepackage{tabulary}
+\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 einen \pgap{\Large \boldgreen{eindeutigen}~~~~} Zusammenhang zwischen zwei Größen oder 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
+$f(x) = \solution{\frac{\delta y}{\delta x}x +t}$ \vspace{0.3cm}\newline
+$f:x \mapsto \solution{mx +t}$ \vspace{0.3cm}\newline
+heißt \boldgreen{lineare Funktion}. \vspace{0.4cm} \newline
+$m :=$ \solution{Steigung} \vspace{0.2cm}\newline
+$y :=$ \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] (\x, {fFunc(\x)});
+  \addplot[domain=-3:4, samples=50, blue] (\x, {gFunc(\x)});
+\end{axis}
+\node at (1, 4) {\textcolor{red}{$f(x) = $}};
+\node at (1, 1.9) {\textcolor{blue}{$g(x) = $}};
+\end{tikzpicture}
+}
+
+\faIcon{pencil-alt} Bestimme die Steigung und die Funktionsterme der Funktionen $f$ und $g$. \\
+\end{tabular}
 
-\begin{center}
-\begin{tabulary}{\textwidth}{C C}
-\includegraphics[keepaspectratio, height=0.48\textheight]{Copyrighted/Fokus9WdhFunktionen.png} &
-\includegraphics[keepaspectratio, height=0.48\textheight]{Copyrighted/Fokus9WdhFunktionen.png} \\
-\includegraphics[keepaspectratio, height=0.48\textheight]{Copyrighted/Fokus9WdhFunktionen.png} &
-\includegraphics[keepaspectratio, height=0.48\textheight]{Copyrighted/Fokus9WdhFunktionen.png} \\
-\end{tabulary}
-\end{center}
+\begin{tabular}{c}
+\begin{tabular}{p{0.5\linewidth} p{0.5\linewidth}}
+\vspace{-4cm}
+Eine Funktion der Form \vspace{0.3cm}\newline
+$f:x \mapsto \frac{a}{x+b} + c$ \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] (\x, {hFunc(\x)});
+  \addplot[domain=1.1:4, samples=200, blue] (\x, {hFunc(\x)});
+\end{axis}
+\node at (0.5, 2.85) {\textcolor{blue}{$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}