import graph_pi;

real f(real x){return -.8x+3;}

graphicrules(unit=1cm,
             xmin=-2, xmax=6, ymin=-2, ymax=6);

draw(graph(f));
draw(graph(new real(real x){return x;}), grey);
cartesianaxis();
draw(recursivegraph(f,-1.8,n=7),.8red);

    
import graph_pi;

real f(real x){return -.8x+3;}

graphicrules(unit=1cm,
             xmin=-2, xmax=6, ymin=-2, ymax=6);

draw(graph(f));
draw(graph(new real(real x){return x;}), grey);
cartesianaxis();
draw(recursivegraph(f,-1.8,n=7),
     //This is the default options
     recursiveoption(L="u",
                    labelbegin=true,
                    labelend=true,
                    labelinner=true,
                    labelalternate=false,
                    format="",
                    labelplace=onX,
                    px=nullpen,
                    py=nullpen,
                    startonyaxis=false,
                    circuitarrow=None,
                    automarker=marker(cross(4)),
                    xaxismarker=nomarker,
                    yaxismarker=nomarker,
                    xmarker=nomarker,
                    fmarker=nomarker),
     .8red);

    
import graph_pi;

real f(real x){return -x^3/8-x^2/4+2x;}

graphicrules(xunit=6cm,yunit=4cm,
             xmin=.9, xmax=2.1, ymin=0, ymax=3);

draw(graph(f));
draw(graph(new real(real x){return x;}), grey);
cartesianaxis(viewyaxis=false);

draw(recursivegraph(f,1,n=5),.8red);

    
import graph_pi;

real f(real x){return -x^3/8-x^2/4+2x;}

graphicrules(xunit=6cm,yunit=4cm,
             xmin=.9, xmax=2.1, ymin=0, ymax=3);

draw(graph(f));
draw(graph(new real(real x){return x;}), grey);
cartesianaxis(xticks=NoTicks,viewyaxis=false);

draw(recursivegraph(f,1,n=5),
     recursiveoption(Label("v", p=blue),
                     labelinner=false),
     .8red);

    
import graph_pi;

real f(real x){return -x^3/8-x^2/4+2x;}

graphicrules(xunit=6cm,yunit=4cm,
             xmin=.9, xmax=2.1, ymin=0, ymax=3);

draw(graph(f));
draw(graph(new real(real x){return x;}), grey);
cartesianaxis(xticks=NoTicks,viewyaxis=false);

draw(recursivegraph(f,1,n=5),
     recursiveoption(Label(scale(.75)*"v"),
                     labelinner=false,
                     format="=%.2f"),
     .8red);

    
import graph_pi;

real f(real x){return -x^3/8-x^2/4+2x;}

graphicrules(unit=2cm,
             xmin=-5, xmax=.25, ymin=-5, ymax=0);

draw(graph(f));
cartesianaxis();
draw(graph(new real(real x){return x;}), grey);

draw(recursivegraph(f,-1.5,n0=1,n=12),
     recursiveoption(Label(scale(.8)*"\alpha",align=2N),
                     px=dashed,
                     xaxismarker=scale(2)*MarkFill[0],
                     automarker=nomarker,
                     circuitarrow=Arrow(position=Relative(.5))),
     .8red);

    
import graph_pi;

real k=3.2;
real f(real x){return k*x*(1-x);}
graphicrules(unit=8cm,
             xmin=0, xmax=1, ymin=0, ymax=1);

draw(graph(f));
cartesianaxis();
draw(graph(new real(real x){return x;}), grey);

draw(recursivegraph(f,.1,n=12),
     recursiveoption(Label("%"),
                     labelplace=onXY,
                     px=dashed+grey,
                     py=dashed+grey,
                     automarker=nomarker,
                     circuitarrow=Arrow(position=Relative(.5),size=2mm)),
     .8red);

    
import graph_pi;

real k=1.5;
real f(real x){return k*x*(1-x);}
graphicrules(xunit=40cm, yunit=20cm,
             xmin=0, xmax=.35, ymin=0, ymax=.35);

draw(graph(f));
cartesianaxis();
draw(graph(new real(real x){return x;}), grey);

draw(recursivegraph(f,.05,n=10),
     recursiveoption(Label("",UnFill),
                     labelalternate=true,
                     px=dashed+grey,
                     format="%.2f"),
     .8red);

    
import graph_pi;

texpreamble("\usepackage{amsmath}");
real k=3.2;
real f(real x){return k*x*(1-x);}
real g(real x){return f(f(x));}
graphicrules(unit=8cm,
             xmin=0, xmax=1, ymin=0, ymax=1);

draw(graph(f),legend="$f:x\longmapsto 3.2x(1-x)$");
draw(graph(g),blue,legend="$g:x\longmapsto{}(f\circ f)(x)$");
cartesianaxis();
draw(graph(new real(real x){return x;}), grey);

draw(recursivegraph(g,.12,n=12),
     recursiveoption(Label("u",align=2S),
                     labelplace=onX,
                     labelinner=false,
                     px=dashed+lightgrey,
                     xmarker=nomarker,
                     circuitarrow=Arrow(position=Relative(.5),size=2mm)),
     .8red, legend="$u_{n+1}=g(u_{n})\;\text{et}\;u_{0}=0.12$");
draw(recursivegraph(g,.6,n=12),
     recursiveoption(Label("v",align=2W),
                     labelplace=onY,
                     labelinner=false,
                     py=dashed+lightgrey,
                     xmarker=nomarker,
                     circuitarrow=Arrow(position=Relative(.5),size=2mm)),
     .8green, legend="$v_{n+1}=g(v_{n})\;\text{et}\;v_{0}=0.6$");
attach(legend(), point(S), 5S);

    
/* Example posted by Olivier Guibé */

import graph_pi;
texpreamble("\usepackage{amsmath}");

real g(real x){return (x^3-1)/5;}
graphicrules(unit=1cm,
             xmin=-1, xmax=4, ymin=-2, ymax=5,
             ycrop=Crop);
draw(graph(g),legend="$g:x\longmapsto (x^3-1)/5$");
cartesianaxis();
draw(graph(new real(real x){return x;}), grey);

draw(recursivegraph(g,2.45,n=4),
     recursiveoption(Label(scale(.8)*"w",UnFill,align=2N),
                     px=dashed,
                     labelinner=false,
                     automarker=nomarker,
                     //              xaxismarker=scale(.2)*MarkFill[0],
                     circuitarrow=Arrow(position=Relative(.5))),.8green,
     legend="$w_{n+1}=g(z_{n})\;\text{et}\;w_{0}=2.45$");

attach(legend(), point(S), N);

    
import graph_pi;

size(10cm,0);

real f(real x){return x^2;};

xlimits(-2, 2);
ylimits(0, 4.25);

draw(graph(f, -2, 2));

/*MODgraph_pi.asy.html#graphpoint(...)MOD*/
graphpoint(Label("$M$",align=NW), f, 1.5);
graphpoint("$P$", f, 1, extendy=true, px=Dotted+red, py=Dotted+blue);
graphpoint("$N$", f, -1, draw=onX, px=Dotted+red);
graphpoint("$Q$", f, sqrt(3), extendx=true);

xaxis(BottomTop(), LeftTicks());
yaxis(Ticks());
yaxis(LeftRight(), Ticks());