Series[(1+δ)^p,{δ,0,4}]

Plot[{1/(1+δ),1-δ},{δ,-.5,.5},PlotRange->All,AxesLabel->{δ,}]

Plot[{1/(Sqrt[1+δ]),1-(1/2)δ},{δ,-.5,.5},PlotRange->All,AxesLabel->{δ,}]

Plot[{1/(Sqrt[1-δ]),1-(-1/2)δ},{δ,-.5,.5},PlotRange->All,AxesLabel->{δ,}]