4. Plot of graphs

y[x_] := x - 1

Plot[y[x], {x, -4, 4}]

y1 = y[x];

y2 = x^2 - x - 4
Plot[{y1, y2}, {x, -4, 4}]

Solve[y1 == y2, x]

Plot of harmonic waves

para = {a ->  7, ω ->  2 Pi 0.5}

yt = a Sin[ω t] /. para

Plot[yt, {t, 0, 10}]

Plot[yt, {t, 0, 10}, AspectRatio ->  0.3]

zu1 = 
      Plot[yt, {t, 0, 10}, AspectRatio -> 0.3, 
        PlotRange -> {{0, 8}, {-8, 8}}, PlotStyle -> Hue[0.9], 
        GridLines -> Automatic, Frame -> True, 
        FrameLabel -> {"t [sec]", "y [m]"}, 
        PlotLabel -> "Fig.1  sine wave"]

zu2 = 
      Plot[Exp[-0.4 t] yt, {t, 0, 10}, 
        PlotStyle -> Hue[0.7]]

Show[zu1, zu2]