Numpy array indexing: view or copy - depends on scope?

Consider the following array manipulations:

import numpy as np
def f(x):
     x += 1
x = np.zeros(1)
f(x)       # changes `x`
f(x[0])    # doesn't change `x`
x[0] += 1  # changes `x`

Why does x[0] behave differently depending on whether += 1 happens inside or outside the function f?

Can I pass a part of the array to the function, such that the function modifies the original array?

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Edit: If we considered = instead of +=, it seems that we would maintain the core of the question while getting rid of some irrelevant complexity.

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