input courbes.mp; %========================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = t**3-6*(t**2)+9*t+2 enddef; %========================================================================= beginfig(1); path p; repere(0,0,-2,5,-2,10,1cm,0.5cm); r_axes; r_origine; p = f_courbe(fx,fy,1,3.8,100); z0 = r_point(1,fy(1)); z1 = r_point(3,fy(3)); label.bot(btex $a$ etex, r_point(1.5,0)); label.bot(btex $b$ etex, r_point(3.4,0)); label.bot(btex $c$ etex, r_point(2,0)); label.lft(btex $f(a)$ etex, r_point(0,fy(1.5))); label.lft(btex $f(b)$ etex, r_point(0,fy(3.4))); label.lft(btex $k=f(c)$ etex, r_point(0,fy(2))); r_point_proj(1.5,fy(1.5)); r_point_proj(3.4,fy(3.4)); r_point_proj(2,fy(2)); draw r_point(0,fy(2))--r_point(4,fy(2)); draw p; pickup pencircle scaled 1.5pt; draw r_point(0,fy(3))--r_point(0,fy(1)); draw r_point(1,0)--r_point(3.8,0); pickup pencircle scaled 0.5pt; label.bot(btex $I$ etex, r_point(3,-0.5)); %label.lft(btex $f(I)$ etex, r_point(-1.2,5)); %draw r_point(0,fy(3))--r_point(3,fy(3)); %draw r_point(0,fy(1))--r_point(4,fy(1)); r_fin; endfig; %========================================================================= vardef fx(expr t) = t enddef; vardef fy(expr t) = t**2 enddef; %========================================================================= beginfig(2); path p; repere(0,0,-2,4,-1,10,1cm,0.5cm); r_axes; r_origine; p = f_courbe(fx,fy,1,3,100); z0 = r_point(1,fy(1)); z1 = r_point(3,fy(3)); label.bot(btex $a$ etex, r_point(1,0)); label.bot(btex $b$ etex, r_point(3,0)); label.bot(btex $c$ etex, r_point(2.3,0)); label.lft(btex $f(a)$ etex, r_point(0,fy(1))); label.lft(btex $f(b)$ etex, r_point(0,fy(3))); label.lft(btex $k=f(c)$ etex, r_point(0,fy(2.3))); r_point_proj(1,fy(1)); r_point_proj(3,fy(3)); r_point_proj(2.3,fy(2.3)); draw p; r_fin; endfig; %========================================================================= beginfig(3); numeric u; u=1cm; z0=(0u,0u); z1=(3u,0u); z2=(1.5u,0.5u); z3=(1.5u,-0.5u); dotlabel.lft(btex $g(y)=x$ etex , z0); dotlabel.rt(btex $y=f(x)$ etex, z1); label.top(btex $f$ etex , z2); label.bot(btex $g$ etex, z3); drawarrow z0..z2..z1; drawarrow z1..z3..z0; endfig; %========================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = ln(t) enddef; %========================================================================== vardef gx(expr t) = t enddef; vardef gy(expr t) = exp(t) enddef; %========================================================================== beginfig(4); path p,q; repere(0,0,-3,3,-3,3,1cm,1cm); %quad_x(0.5,1,black); %quad_y(0.5,1,black); pickup pencircle scaled 1.2pt; drawarrow (_r_xmin,_oy)..(_r_xmax,_oy); drawarrow (_ox,_r_ymin)..(_ox,_r_ymax); % pickup pencircle scaled 0.5pt; % label.bot(btex $x$ etex, (_r_xmax-1mm,_oy)); % label.lft(btex $y$ etex, (_ox,_r_ymax-1mm)); r_origine; %r_axes; z1=r_point(0,exp(1)); z2=r_point(0,exp(0)); label.lft(btex $y$ etex, z2); z3=r_point(1,0); label.bot(btex $y$ etex, z3); z4=r_point(exp(1),0); z5=r_point(1,exp(1)); z6=r_point(exp(1),1); draw z1--z5--z3 dashed evenly; draw z2--z6--z4 dashed evenly; dotlabel(btex $$ etex,z5); dotlabel(btex $$ etex,z6); draw z5--z6 dashed evenly; %dotlabel(btex $$ etex,r_point(1,1)); label.top(btex $C_{f}$ etex, r_point(1.5,-2)); label.top(btex $y=x$ etex, r_point(-1.5,-2.5)); label.bot(btex $C_{g}$ etex, r_point(-2.2,1)); label.lft(btex $x$ etex, z1); label.bot(btex $x$ etex, z4); pickup pencircle scaled 0.8pt; p = f_courbe(fx,fy,0.1353,2.7182,100); q = f_courbe(gx,gy,-2,1,100); draw p; draw q;% withcolor blue ; draw r_droitedir(0,0,1); r_fin; endfig; %========================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = t**2-2*t enddef; %========================================================================= vardef gx(expr t) = t enddef; vardef gy(expr t) = t-2 enddef; %========================================================================== vardef hx(expr t) = t enddef; vardef hy(expr t) = t**2 enddef; %========================================================================== beginfig(5); path p,q; repere(0,0,-2,6,-3,5,1cm,0.5cm); r_axes; r_origine; p = f_courbe(fx,fy,-2,1,100); q = f_courbe(gx,gy,1,4,100); draw p; draw q; endfig; %========================================================================== beginfig(6); path p,q; repere(0,0,-2,6,-3,5,1cm,0.5cm); r_axes; r_origine; p = f_courbe(hx,hy,-2,1,100); q = f_courbe(gx,gy,1,4,100); draw p; draw q; draw r_point(1,hy(1))--r_point(1,gy(1)) dashed evenly; dotlabel(btex $$ etex, r_point(1,hy(1))); endfig; %========================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = t**3-6*(t**2)+9*t+2 enddef; %========================================================================= beginfig(11); path p; repere(0,0,-2,5,-2,10,1cm,0.5cm); r_axes; r_origine; p = f_courbe(fx,fy,1,3.8,100); z0 = r_point(1,fy(1)); z1 = r_point(3,fy(3)); r_point_proj(1,fy(1)); r_point_proj(3,fy(3)); r_point_proj(3.8,fy(3.8)); draw p; pickup pencircle scaled 1.5pt; draw r_point(0,fy(3))--r_point(0,fy(1)); draw r_point(1,0)--r_point(3.8,0); pickup pencircle scaled 0.5pt; label.bot(btex $I$ etex, r_point(3,-0.5)); label.lft(btex $f(I)$ etex, r_point(-1.2,5)); %draw r_point(0,fy(3))--r_point(3,fy(3)); %draw r_point(0,fy(1))--r_point(4,fy(1)); r_fin; endfig; end