Plot[x/(x^2+1),{x,-5,5},
PlotStyle->Thick,
Epilog->{
PointSize[.03],Point[{{-1,-1/2},{1,1/2}}]
}
]

Plot[Sin[x],{x,-2Pi,2Pi},
PlotStyle->Thick,
Epilog->{
PointSize[.03],Point[{{Pi/2,1},{-3Pi/2,1},{-Pi/2,-1},{3Pi/2,-1}}]
}
]

Plot[x^2-3,{x,-3,3},
PlotStyle->Thick,
Epilog->{PointSize[.03],Point[{0,-3}],
Text[Style["min",Large],{.5,-1.8}]}]

Plot[{(x^2-1)/(x^2+1),1},{x,-8,8},
PlotStyle->{{Thick},{Thick,Dashed}},
PlotRange->{-1,1},
Epilog->{PointSize[.03],Point[{0,-1}]}]

Plot[3-x^2,{x,-3,3},
PlotStyle->Thick,
Epilog->{
PointSize[.03],Point[{0,3}]
}
]

Plot[3,{x,-3,3},PlotStyle->{Thick}]

Plot[x^4-8x^2+16,{x,-3,3},
PlotStyle->Thick,
Epilog->{
PointSize[.03],Point[{{-2,0},{2,0},{0,16}}]
}
]

Plot[CubeRoot[x^2]*CubeRoot[6-x],{x,-2,10},
PlotStyle->Thick,
Epilog->{
PointSize[.03],Point[{{0,0},{4,2^(5/3)},{6,0}}]
}
]

Plot[x^5 - 4x^3 + 4x + 7,{x,-2,2},
PlotStyle->Thick,
Epilog->{
{
PointSize[.03],Red,Point[{
{-Sqrt[2/5],7-((64 (Sqrt[(2/5)]))/25)},{Sqrt[2/5],7+((64 (Sqrt[(2/5)]))/25)},{-Sqrt[2],7},{Sqrt[2],7}
}]},

PointSize[.03],Black,Point[{
{0,7},{-Sqrt[6/5],7-((16 (Sqrt[(6/5)]))/25)},{Sqrt[6/5],7+((16 (Sqrt[(6/5)]))/25)}
}]
}
]