How do you plot piecewise functions?

Questions
,
1

Can you plot (on the same graph) a piecewise function in Mathematica? Not several functions over the same domain, but different functions over
non-intersecting domains. A simple example: f:= 2x - 3 for -4 <= x <= 1, and g[x_}:= -7x + 2 for 1 < x <= 5.

2 
(* Clear memory. *)
Clear["Global`*"];

(* Define piecewise functions. *)
f[x_] := Piecewise[{ {2x-3, -4 <= x <= 1} }];
g[x_] := Piecewise[{ {-7x+2, 1 < x <= 5} }];

(* Plot. *)
Plot[ {f[x],g[x]}, {x, -5, 5}]
3

This solution is not always works ideally. Somewhy Piecewise functions can have gaps while plotting. Check out this code, It can even be some faster

MembershipFunction[center_, mid_] := 
 Module[{S, pi}, 
  pi[x_, a_, c_] := Piecewise[{
          {S[x, c - b, c - b/2, c] /. {b -> (a + c)/2},     x <= c}, 
          {1 - S[x, c, c + b/2, c + b] /. {b -> (a + c)/2}, x > c}}];
  S[x_, a_, b_, c_] := Piecewise[{
         {0, x < a}, 
         {2 ((x - a)/(c - a))^2,    a <= x <= b}, 
         {1 - 2 ((x - c)/(c - a))^2, b < x <= c}, 
         {1, x > c}}];
  a = 4 (3/4 center - mid);
  ListLinePlot[Table[{x, pi[x, a, center]}, {x, 0, center*2, center/50}]]
 ]
4

Your functions can be combined into one well defined piecewise function, In the following {0,True) assigns the value zero to the function outside the defined intervals:

pw[x_] :=  Piecewise[{{2 x - 3 , -4 <= x <= 1}, {-7 x + 2 , 1 < x <= 5}, {0,True}}]

You can plot this (as desired). I have used ExclusionStyle to show the discontinuities:

Plot[pw[x], {x, -10, 10}, ExclusionsStyle -> {{Red, Dashed}, Blue}]
5

The other option..