If f(x) = |x| + |x – 1|, then which one of the followings is correct?

1
f(x) is continuous at x = 0 and x = 1
2
f(x) is continuous at x = 0 but not at x = 1
3
f(x) is continuous at x = 1 but not at x = 0
4
f(x) is neither continuous at x = 0 nor at x = 1

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