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.