ϵ = 1;
δ =  .2;
a = 2;
l = 4;
Plot[{x^2, l + ϵ, l - ϵ}, {x, a - δ, 
        a +  δ}, 
      PlotStyle -> {RGBColor[0, 0, 0], RGBColor[1, 0, 0], 
          RGBColor[1, 0, 0]}]

ϵ = 1;
δ = 1;
a = 3;
l = 32;
Plot[{3  x^2 + 2  x - 1, l + ϵ, l - ϵ}, {x, 
        a - δ, a +  δ}, 
      PlotStyle -> {RGBColor[0, 0, 0], RGBColor[1, 0, 0], 
          RGBColor[1, 0, 0]}]

ϵ = 1;
δ = 3;
a = 1;
l = 0;
Plot[{x^3 - 1, l + ϵ, l - ϵ}, {x, a - δ, 
        a +  δ}, 
      PlotStyle -> {RGBColor[0, 0, 0], RGBColor[1, 0, 0], 
          RGBColor[1, 0, 0]}]

ϵ = 2;
δ = 1;
a = -1;
l = -1;
Plot[{x^4 + 2  x, l + ϵ, l - ϵ}, {x, a - δ, 
        a +  δ}, 
      PlotStyle -> {RGBColor[0, 0, 0], RGBColor[1, 0, 0], 
          RGBColor[1, 0, 0]}]