?Plot

Plot[x^2,{x,-1,1}]

Plot[x^2,{x,-2,2}]

Plot[x^2,{x,-2,2},AspectRatio->Automatic]

Options[Plot]

Plot[x^2Cos[x],{x,-2,2},AspectRatio->Automatic]

Plot[x^2Cos[1/x],{x,-2,2},AspectRatio->Automatic]

Plot[x^2Cos[1/x],{x,-2,2},AspectRatio->Automatic,PlotRange->{{-0.1,0.1},{-0.1,0.1}}]

f[x_]:=(x^2+1)/x^3

Plot[f[x],{x,-2,2}]

Manipulate[Plot[f[x],{x,-2,2},Epilog->Point[{k,f[k]}]],{k,-2,2}]

Plot3D[x*Cos[y(x-1)/x],{x,-2,2},{y,0,1},AspectRatio->Automatic]

Plot3D[Cos[x*y],{x,-Pi,Pi},{y,-Pi,Pi},AspectRatio->Automatic]

Plot3D[Cos[x*y],{x,-2Pi,2Pi},{y,-2Pi,2Pi},AspectRatio->Automatic]

f[a_,b_][{x_,y_}]:={a-x^2+b*y,x}

f[1,1][{0.3,1.2}]

orbita[{{x0_,y0_},a_,b_},nmax_]:=
Block[{k,lista={} ,punto={x0,y0}},
For[k=1,k≤ nmax, k++,
AppendTo[lista, punto];
punto=f[a,b][punto];
];
Return[lista];
]

orbitafin[{{x0_,y0_},a_,b_},nmax_]:=
Block[{k,lista={} ,punto={x0,y0}},
k=1;
While[Norm[punto]<10&&k≤ nmax,
AppendTo[lista, punto];
punto=f[a,b][punto];
k++;
];
Return[lista];
];

Manipulate[Graphics[{PointSize[.01],Point[orbitafin[{{x0,y0},a,b},n]]},PlotRange->{{-2,2},{-2,2}}],{{x0,.2},-2,2},{{y0,-.5},-2,2},{{a,.31},0,2},{{b,1},0,2},{{n,3},1,10000,1}]

Manipulate[Graphics[{PointSize[.005],Point[orbita[{{x0,y0},a,b},n]]},PlotRange->{{-2,2},{-2,2}}],{{x0,.2},-2,2},{{y0,-.5},-2,2},{{a,1.4},0,2},{{b,.3},0,2},{{n,1000},1,10000,1}]

Manipulate[Graphics[{PointSize[.005],Point[orbitafin[{{x0,y0},a,b},n]]},PlotRange->{{-2,2},{-2,2}}],{{x0,.2},-2,2},{{y0,-.5},-2,2},{{a,.31},0,2},{{b,1},0,2},{{n,1000},1,10000,1}]