It is evident that f is defined at all points of the real line. Let c be a real number.
Case I:
Therefore, f is continuous at all points x, such that x < 0
Case II:
Therefore, f is continuous at all points x, such that x > 0
Case III:
Therefore, f is continuous at x = 0
From the above observations, it can be concluded that f is continuous at all points of the real line. Thus, f has no point of discontinuity.
