While Joe Kington certainly proposes the most sensible answer when he recommends that only the necessary data be plotted, there are situations where it would be best to plot all of the data and just zoom to a certain section. Additionally, it would be nice to have an “autoscale_y” function that only requires the axes object (i.e., unlike the answer here, which requires direct use of the data.)

Here is a function that just rescales the y-axis based on the data that is in the visible x-region:

```
def autoscale_y(ax,margin=0.1):
"""This function rescales the y-axis based on the data that is visible given the current xlim of the axis.
ax -- a matplotlib axes object
margin -- the fraction of the total height of the y-data to pad the upper and lower ylims"""
import numpy as np
def get_bottom_top(line):
xd = line.get_xdata()
yd = line.get_ydata()
lo,hi = ax.get_xlim()
y_displayed = yd[((xd>lo) & (xd<hi))]
h = np.max(y_displayed) - np.min(y_displayed)
bot = np.min(y_displayed)-margin*h
top = np.max(y_displayed)+margin*h
return bot,top
lines = ax.get_lines()
bot,top = np.inf, -np.inf
for line in lines:
new_bot, new_top = get_bottom_top(line)
if new_bot < bot: bot = new_bot
if new_top > top: top = new_top
ax.set_ylim(bot,top)
```

This is something of a hack, and will probably not work in many situations, but for a simple plot, it works well.

Here is a simple example using this function:

```
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-100,100,1000)
y = x**2 + np.cos(x)*100
fig,axs = plt.subplots(1,2,figsize=(8,5))
for ax in axs:
ax.plot(x,y)
ax.plot(x,y*2)
ax.plot(x,y*10)
ax.set_xlim(-10,10)
autoscale_y(axs[1])
axs[0].set_title('Rescaled x-axis')
axs[1].set_title('Rescaled x-axis\nand used "autoscale_y"')
plt.show()
```