input courbes.mp;
%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                (-0.5)*(t**3)+(2.25)*(t**2)-(0.5)*t-2
enddef;
%=============================================================================
verbatimtex 
%&latex 
\documentclass{article} 
\usepackage{palatino} 
\newcommand{\vect}[1]{\overrightarrow{#1}}
\newcommand{\Vect}[1]{\overrightarrow{\strut #1}}
\begin{document} 
etex 
                
beginfig(1);
path p; 
repere(0,0,-1,3,-3,5,1cm,0.5cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(-1,3,100);
z0 = r_point(2,0);
z1 = r_point(0,fy(2));
r_point_proj(2,fy(2));
r_ppoint(2,fy(2));
label.bot(btex $x$ etex,z0);
label.lft(btex $f(x)$ etex,z1);
draw p;
r_fin;
endfig;

%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                sqrt(t+2)
enddef;
%=============================================================================

beginfig(2);   
path p; 
repere(0,0,-2,5,-1,3,1cm,1cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(-1.8,5,100);
z0 = r_point(1,0);
z1 = r_point(0,fy(1));
r_point_proj(1,fy(1));
r_ppoint(1,fy(1));
z2 = r_point(4,0);
z3 = r_point(0,fy(4));
r_point_proj(4,fy(4));
r_ppoint(4,fy(4));
label.bot(btex $u$ etex,z0);
label.lft(btex $f(u)$ etex,z1);
label.bot(btex $v$ etex,z2);
label.lft(btex $f(v)$ etex,z3);
draw p;
r_fin;
endfig;


%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                -(t**2)-(4*t)-1.5
enddef;
%=============================================================================

beginfig(3);
 
path p; 
repere(0,0,-2,1,-5,3,2cm,0.5cm);
%quad_x(1);
%quad_y(1);
r_axes;
r_origine;
%r_unites;
p = f_courbe(-2,1,100);
z0 = r_point(-1,0);
z1 = r_point(0,fy(-1));
r_point_proj(-1,fy(-1));
r_ppoint(-1,fy(-1));
z2 = r_point(0.5,0);
z3 = r_point(0,fy(0.5));
r_point_proj(0.5,fy(0.5));
r_ppoint(0.5,fy(0.5));
label.bot(btex $u$ etex,z0);
label.rt(btex $f(u)$ etex,z1);
label.top(btex $v$ etex,z2);
label.lft(btex $f(v)$ etex,z3);
draw p;
r_fin;
endfig;

end