Functions intervals

I have 3 functions, how can I plot them using differents intervals ?

This is my code:

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(-5,5,100)
y = 2*x+1
k = 3*x+2
i = 2*x+2
plt.plot(x, y, '-r', label='y=2x+1')
plt.plot(x, k, '-r', label='k =3x+2')
plt.plot(x, i, '-r', label='i =2x+2')
plt.title('3 functions on 3 intervals')
plt.xlabel('x', color='#1C2833')
plt.ylabel('y', color='#1C2833')
plt.legend(loc='upper left')
plt.grid()
plt.show()

This is the style I need :

This is what I get :

My wish is to draw the first function 2*x+1 on the following interval [x:2->x:8].

The second function 3*x+2 has to be plotted on the interval [x:8->x:12]

The third function 2*x+2 has to be plotted on the interval [x:12->x:20]

Is it possible ?

>Solution :

Is it this that you want?

In [33]: import matplotlib.pyplot as plt
    ...: import numpy as np
    ...: 
    ...: xs = [np.linspace(0,4), np.linspace(-3, 5), np.linspace(4, 10)]
    ...: fs = [np.cos, np.sin, lambda x:np.sin(x)-2*np.cos(x)]
    ...: for x, f in zip(xs, fs):
    ...:     plt.plot(x, f(x), label=f.__name__)
    ...: plt.legend()
    ...: plt.show()