Exponential

{xmin, xmax} = {-4, 3};
frame[t_] := (With[{a = (xmax + xmin)/2 +
       0.5 (xmax - xmin - 2.4) Sin[2 Pi t]},
    Show[
     Graphics[{
       {
        Darker@Blue,
        Line[{{a, Exp[a]} - 100 {1, Exp[a]}, {a, Exp[a]} +
           100 {1, Exp[a]}}],
        Line[{{a, -5}, {a, 8}}],
        Line[{{xmin - 1, 0}, {xmax + 1, 0}}],
        },
       {
        Darker@Red,
        PointSize[Medium],
        Point[{a - 1, 0}],
        Point[{a, Exp[a]}]
        },
       {
        FaceForm[Directive[Opacity[0.4], RGBColor[0.2, 0.3, 0.4]]],
        EdgeForm[RGBColor[0, 0.2, 0.3]],
        Disk[{a, 0}, 1]}
       },
      PlotRange -> {{xmin - 1, xmax + 1}, {-1, 7}},
      ImagePadding -> 10
      ],
     Plot[Exp[x], {x, xmin - 1, xmax + 1},
      PlotStyle -> Directive[Darker@Red, Thick]]
     ]
    ]);
Manipulate[
 frame[t],

 {t, 0, 1}]