input courbes.mp;
verbatimtex 
%&latex 
\documentclass{article} 
\newcommand{\vect}[1]{\overrightarrow{#1}}
\newcommand{\Vect}[1]{\overrightarrow{\strut #1}}
\begin{document} 
etex 

%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                1/(t-1) +1
enddef;
%=============================================================================
%============================================================================
vardef gx(expr t) =
t
enddef;
vardef gy(expr t) =
                1/(1-t) +0.5
enddef;
%=============================================================================

beginfig(1);   
path p,q; 
repere(0,0,-1,4,-1,5,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,1.1,4,100);
q = f_courbe(gx,gy,-1,0.9,100);
z0 = r_point(2,fy(2));
z1 = r_point(0,fy(2));
z2 = r_point(0,fy(2));
z3 = r_point(2,0);
z4 = r_point(2,5);
z5 = r_point(0,fy(1.5));
z6 = r_point(1.7,fy(1.7));
z66 = r_point(1.5,fy(1.5));
z7 = r_point(1,0);
z77 = r_point(1.5,0);
z8 = r_point(1/3,0);
z88 = r_point(0.7,0);
z9 = r_point(1/3,gy(1/3));
z99 = r_point(0.5,gy(0.5));
z999 = r_point(0.7,gy(0.7));
z10 = r_point(1/3,5);

draw z3--z4 dashed evenly;
draw z8--z10 dashed evenly;
draw rx_droite(1);
draw r_droitedir(0,fy(2),0);

label.llft(btex $a$ etex, z7);
label.bot(btex $x$ etex, z3);
label.bot(btex $x$ etex, z8);
label.llft(btex $M$ etex, z2);
label.ulft(btex $f(x)$ etex, z2);
label.top(btex $C_{f}$ etex, r_point(3,1));

draw p;draw q;

pickup pencircle scaled 1.5pt;
drawarrow z1--z5;
drawarrow z0...z6...z66;
drawarrow z3--z77;
drawarrow z8--z88;
drawarrow z9...z99...z999;

%r_labelxy;
r_fin;
endfig;


%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                exp(t)
enddef;
%=============================================================================



beginfig(2);   
path p; 
repere(0,0,-1,4,-1,5,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,-1,4,100);
z0 = r_point(1,fy(1));
z1 = r_point(0,fy(1));
z2 = r_point(0,fy(1.5));
z3 = r_point(1,0);
z4 = r_point(1.5,0);
z5 = r_point(1.5,fy(1.5));
z6 = r_point(1,5);



draw z3--z6 dashed evenly;
draw r_droitedir(0,fy(1),0);

label.bot(btex $x$ etex, z3);
label.llft(btex $M$ etex, z1);
label.ulft(btex $f(x)$ etex, z1);
label.top(btex $C_{f}$ etex, r_point(-0.5,1));

draw p;

pickup pencircle scaled 1.5pt;
drawarrow z1--z2;
drawarrow z0...z5;
drawarrow z3--z4;


%r_labelxy;
r_fin;
endfig;



%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                -exp(t)
enddef;
%=============================================================================



beginfig(3);   
path p; 
repere(0,0,-1,4,-5,1,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,-1,4,100);
z0 = r_point(1,fy(1));
z1 = r_point(0,fy(1));
z2 = r_point(0,fy(1.5));
z3 = r_point(1,0);
z4 = r_point(1.5,0);
z5 = r_point(1.5,fy(1.5));
z6 = r_point(1,-5);


draw z3--z6 dashed evenly;
draw r_droitedir(0,fy(1),0);

label.top(btex $x$ etex, z3);
label.ulft(btex $M$ etex, z1);
label.llft(btex $f(x)$ etex, z1);
label.top(btex $C_{f}$ etex, r_point(-0.5,1));

draw p;

pickup pencircle scaled 1.5pt;
drawarrow z1--z2;
drawarrow z0...z5;
drawarrow z3--z4;


%r_labelxy;
r_fin;
endfig;

%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                1/(t-1) +1
enddef;
%=============================================================================
                
beginfig(4);   
path p,q; 
repere(0,0,-1,4,-1,5,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,1.1,4,100);
z0 = r_point(2,fy(2));
z1 = r_point(0,fy(2));
z2 = r_point(0,fy(2));
z3 = r_point(2,0);
z4 = r_point(2,5);
z5 = r_point(0,fy(1.5));
z6 = r_point(1.7,fy(1.7));
z66 = r_point(1.5,fy(1.5));
z7 = r_point(1,0);
z77 = r_point(1.5,0);


draw z3--z4 dashed evenly;
draw rx_droite(1);
draw r_droitedir(0,fy(2),0);

label.llft(btex $a$ etex, z7);
label.bot(btex $x$ etex, z3);
label.llft(btex $M$ etex, z2);
label.ulft(btex $f(x)$ etex, z2);
label.top(btex $C_{f}$ etex, r_point(3,1));

draw p;

pickup pencircle scaled 1.5pt;
drawarrow z1--z5;
drawarrow z0...z6...z66;
drawarrow z3--z77;

%r_labelxy;
r_fin;
endfig;


           
%============================================================================
vardef gx(expr t) =
t
enddef;
vardef gy(expr t) =
                1/(1-t) +0.5
enddef;
%=============================================================================

beginfig(5);   
path q; 
repere(0,0,-1,4,-1,5,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
q = f_courbe(gx,gy,-1,0.9,100);

z2 = r_point(0,gy(1/3));
z5 = r_point(0,gy(0.7));
z7 = r_point(1,0);
z8 = r_point(1/3,0);
z88 = r_point(0.7,0);
z9 = r_point(1/3,gy(1/3));
z99 = r_point(0.5,gy(0.5));
z999 = r_point(0.7,gy(0.7));
z10 = r_point(1/3,5);

draw z8--z10 dashed evenly;
draw rx_droite(1);
draw r_droitedir(0,gy(1/3),0);

label.llft(btex $a$ etex, z7);
label.bot(btex $x$ etex, z8);
label.llft(btex $M$ etex, z2);
label.ulft(btex $f(x)$ etex, z2);
label.top(btex $C_{f}$ etex, r_point(-0.5,0.5));

draw q;

pickup pencircle scaled 1.5pt;
drawarrow z2--z5;
drawarrow z8--z88;
drawarrow z9...z99...z999;

%r_labelxy;
r_fin;
endfig;


%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                (1/t) +1
enddef;
%=============================================================================

beginfig(6);   
path p;
numeric _a;
repere(0,0,-1,4,-1,5,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,0.1,4,100);

z0 = r_point(1.5,0);
z1 = r_point(1.5,1);
_a = 2-(fy(1.5));
z2 = r_point(1.5,fy(1.5));
z3 = r_point(0,fy(1.5));
z4 = r_point(0,1);
z5 = r_point(0,_a);
z6 = r_point(2,0);
z7 = r_point(2,fy(2));

draw z0--z2 dashed evenly;
draw r_droitedir(0,1,0);
draw r_droitedir(0,fy(1.5),0) dashed evenly;
draw r_droitedir(0,_a,0) dashed evenly;

label.bot(btex $x$ etex, z0);
dotlabel.llft(btex $P$ etex, z1);
dotlabel.top(btex $M$ etex, z2);
label.top(btex $l+\alpha$ etex, z3-r_point(0.5,0));
label.top(btex $l$ etex, z4-r_point(0.5,0));
label.top(btex $l-\alpha$ etex, z5-r_point(0.5,0));
label.top(btex $C_{f}$ etex, r_point(0.8,fy(0.8)+0.4));

draw p;

pickup pencircle scaled 1.5pt;
drawarrow z0--z6;
drawarrow z2--z7;

%r_labelxy;
r_fin;
endfig;



%============================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
               t+1+2/(t+2)
enddef;
%=============================================================================
%============================================================================
vardef gx(expr t) =
t
enddef;
vardef gy(expr t) =
                t+1
enddef;
%=============================================================================

beginfig(7);   
path p,q;
numeric _a;
repere(0,0,-2,5,-1,6,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(fx,fy,-1.9,5,100);
q = f_courbe(gx,gy,-2,5,100);

z0 = r_point(3,0);
z2 = r_point(3,fy(3));
z1 = r_point(3,gy(3));
z3 = r_point(0,fy(3));
z4 = r_point(0,gy(3));

draw z0--z2 dashed evenly;
draw z1--z4 dashed evenly;
draw z2--z3 dashed evenly;



label.bot(btex $x$ etex, z0);
dotlabel.lrt(btex $P$ etex, z1);
dotlabel.top(btex $M$ etex, z2);
label(btex $f(x)$ etex, z3-r_point(0.5,0));
label(btex $ax+b$ etex, z4-r_point(0.5,0));
label.top(btex $C_{f}$ etex, r_point(-0.5,1.2));

draw p;draw q;

%r_labelxy;
r_fin;
endfig;





end