By the options we can conclude that we have to examine the continuity of this function at x = 0 and x = 1.

We can do this by finding the limits of the functions slightly above and below each of these points.

f(x) = |x − 1| + |x + 1|



For x = 0



∴ f(x) is continuous at x = 0

For x = 1



∴ f(x) is continuous at x = 1.

∴ f(x) is continuous at both x = 0 and 1.

Hence, option 1.