Identify the correct option (s)

A. A modulus function is continuous at every point in its domain.
B. A modulus function may or may not be continuous at every point in its domain.
C. Every rational function is continuous in its domain.
D. If a function f is differentiable at a point then it is also continuous at that point.
E. If a function f is continuous at a point then it is also differentiable at that point.

Choose the correct answer from the options given below :

A, C and D only

(B) → incorrect

(E) → incorrect → continuous function is not always differentiable e.g. |x| → continuous at x = 0 but NOT differentiable at x = 0