I want to superpose two graphs where x-axis corresponds. The first is on the full range, while second is upon a sub-interval.

test1 = pd.DataFrame(
    {
        'x': [1,2,3,4,5,6,7,8,9],
        'y': [0,1,1,2,1,2,1,1,1]
    }
)

test2 = pd.DataFrame(
    {
        'x': [1,2,4,5,8],
        'y': [3,2,2,3,3]
    }
)

>Solution :

You can use the xlim() function in matplotlib.

Example:

import matplotlib.pyplot as plt
import pandas as pd

test1 = pd.DataFrame(
    {
        'x': [1,2,3,4,5,6,7,8,9],
        'y': [0,1,1,2,1,2,1,1,1]
    }
)

test2 = pd.DataFrame(
    {
        'x': [1,2,4,5,8],
        'y': [3,2,2,3,3]
    }
)

plt.plot(test1['x'], test1['y'], 'b-', label='test1')
plt.plot(test2['x'], test2['y'], 'r-', label='test2')
plt.xlim(min(test1['x']), max(test1['x']))
plt.legend()
plt.show()

Result: https://i.stack.imgur.com/bz41W.png