\input preamble.tex

\Defdim(\k,-0.7)
\newdimen\a
\newdimen\b
\newdimen\x
\newdimen\y

\def\dsp{\displaystyle}

% -------------------------------------------------------------------------
\begin{document}
\unitlength1.3cm

\begin{center}
{\huge \bf{Curve Family I}}
\bigskip

\begin{lapdf}(14,14)(-7,-7)
 \Lingrid(10)(1,3)(-7,7)(-7,7)
 \Rect(-7,-7,14,14)
 \Setclip
 \def\FamilyI(#1){\Polynom(-7,+7)(0.1,#1,0,#1) \Stroke}
 \Whiledim{\k<0.8}{\Stepcol(0,23,2) \FamilyI(\Np\k) \Dadd(\k,0.1)}
 \Setwidth(0.01)
 \Black
 \Dash(1)
 \Polynom(-7,+7)(-0.05,0,-0.15,0) \Stroke
 \Dash(0)
 \Point(1)(+4.67,-5.78)
 \Point(1)(+4.00,-3.80)
 \Point(1)(+3.33,-2.35)
 \Point(1)(+2.67,-1.35)
 \Point(1)(+2.00,-0.70)
 \Point(1)(+1.33,-0.32)
 \Point(1)(+0.67,-0.11)
 \Point(1)(+0.00,+0.00)
 \Point(1)(-0.67,+0.11)
 \Point(1)(-1.33,+0.32)
 \Point(1)(-2.00,+0.70)
 \Point(1)(-2.67,+1.35)
 \Point(1)(-3.33,+2.35)
 \Point(1)(-4.00,+3.80)
 \Point(1)(-4.67,+5.78)
 \Text(-5.8,5,rb){$k=7$}
 \Text(5.8,-5,lt){$k=-7$}
 \Text(-4.6,6.2,lb){$f_{e}(x)=-\dsp\frac{1}{20}(x^3+3x)$}
\end{lapdf}

$f_{k}(x)=\dsp\frac{1}{10}(x^3+kx^2+k)$ \qquad $k = -7 \dots +7$

\newpage

{\huge \bf{Curve Family II}}
\bigskip

\begin{lapdf}(14,14)(-7,-7)
 \Lingrid(10)(1,3)(-7,7)(-7,7)
 \Rect(-7,-7,14,14)
 \Setclip
 \def\FamilyII(#1){\Polynom(-7,+7)(0.1,#1,0.1,0) \Stroke}
 \Whiledim{\k<0.8}{\Stepcol(0,23,2) \FamilyII(\Np\k) \Dadd(\k,0.1)}
 \Setwidth(0.01)
 \Black
 \Dash(1)
 \Polynom(-7,+7)(-0.05,0,0.05,0) \Stroke
 \Dash(0)
 \Point(1)(+4.59,-4.62)
 \Point(1)(+3.91,-2.80)
 \Point(1)(+3.23,-1.52)
 \Point(1)(+2.54,-0.69)
 \Point(1)(+1.82,-0.21)
 \Point(1)(+1.00,+0.00)
 \Point(1)(+0.00,+0.00)
 \Point(1)(-1.00,+0.00)
 \Point(1)(-1.82,+0.21)
 \Point(1)(-2.54,+0.69)
 \Point(1)(-3.23,+1.52)
 \Point(1)(-3.91,+2.80)
 \Point(1)(-4.59,+4.62)
 \Text(-5.6,4.1,rb){$k=7$}
 \Text(5.6,-4.1,lt){$k=-7$}
 \Text(-4.9,6.2,lb){$f_{e}(x)=-\dsp\frac{1}{20}(x^3-x)$}
\end{lapdf}

$f_{k}(x)=\dsp\frac{1}{10}(x^3+kx^2+x)$ \qquad $k = -7 \dots +7$

\newpage

{\huge \bf{Curve Family III}}
\bigskip

\begin{lapdf}(13,11)(-5,-3)
 \Lingrid(10)(1,3)(-5,8)(-3,8)
 \Rect(-5,-3,13,11)
 \Setclip
 \def\Fx(#1,#2){\Dset(\x,#1) \y=2\k \Sub(\y,\x)
  \Exp(\Np\y,#2) \Add(#2,\x) \y=3\k \Sub(#2,\y)}
 \Dset(\k,-1)
 \Whiledim{\k<3.5}{
  \a=\k \Dsub(\a,3.25) \b=\k \Dadd(\b,8) 
  \Stepcol(0,23,2) \Fplot(96)(\Np\a,\Np\b) \Stroke \Dadd(\k,0.5)}
 \Setwidth(0.01)
 \Black
 \Dash(1)
 \Polynom(-4,+7)(0,0,-0.5,1) \Stroke
 \Dash(0)
 \Point(1)(-2.0,+2.0)
 \Point(1)(-1.0,+1.5)
 \Point(1)(+0.0,+1.0)
 \Point(1)(+1.0,+0.5)
 \Point(1)(+2.0,+0.0)
 \Point(1)(+3.0,-0.5)
 \Point(1)(+4.0,-1.0)
 \Point(1)(+5.0,-1.5)
 \Point(1)(+6.0,-2.0)
 \Text(-4.7,7.7,lt){$k=-1$}
 \Text(+2.9,7.7,lt){$k=+3$}
 \Text(-4.9,2.1,lb){$y_e=1-\dsp\frac{x}{2}$}
\end{lapdf}

$f_{k}(x)=e^{\dsp{2k-x}}+x-3k$ \qquad $k = -1 \dots +3$
\end{center}
\end{document}
