f[x_] = 1 /(1+ 25x^2)

Plot[f[x], {x, -1, 1}]

data= Table[{0.2 i, f[0.2 i]},
{i, -5, 5}]

Clear[g,Q];
g[x_]= InterpolatingPolynomial[data, x];
Q[x] = Expand[g[x]]

dots = ListPlot[data,PlotStyle->{PointSize[0.02]},
        DisplayFunction->Identity];
g1=Plot[{f[x], g[x]}, {x, -1.1,1.1},
DisplayFunction->Identity];
Show[g1,dots,PlotRange->{{-1.1,1.1},
 {-0.4,2}},
PlotLabel->"f(x) and the interpolating polynomial.",
AxesLabel->{"x","y"},DisplayFunction->$DisplayFunction];

dots = ListPlot[data,PlotStyle->
{PointSize[0.02]},
         DisplayFunction->Identity];
g1=Plot[{f[x], g[x]}, {x, -1.25,1.25},
DisplayFunction->Identity];
Show[g1,dots,PlotRange->{{-1.25,1.25},
  {-4,2}},
PlotLabel->"f(x) and the interpolating polynomial.",
AxesLabel->{"x","y"},DisplayFunction->$DisplayFunction];

Clear[data];
data= Table[{Cos[(2i+1) Pi /20]//N, 
f[Cos[(2i+1) Pi /20]//N]},{i, 0, 9}]

g[x_]= InterpolatingPolynomial[data, x];
Q[x] = Expand[g[x]]

dots = ListPlot[data,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
g1=Plot[{f[x], g[x]}, {x, -1,1},
DisplayFunction->Identity];
Show[g1,dots,PlotRange->{{-1,1},{0,1}},
PlotLabel->"f(x) and the interpolating polynomial.",
AxesLabel->{"x","y"},DisplayFunction->$DisplayFunction];