(* Q1(a) solution *)
y1[x_]:=Tan[x];
Plot[y1[x],{x,-Pi/2,Pi/2},AxesLabel->{"x","Tan[x]"}]

y[x_]:=ArcTan[x];
Plot[y[x],{x,-5Pi,5Pi},AxesLabel->{"x","ArcTan[x]"}]

Domain of ArcTan[x] = (-∞,∞);
Range of ArcTan[x] = (-π/2,π/2);