Which of the following statements is true for the function $f(x) = \begin{cases} x^2 + 3, & x \neq 0 \\ 1 &, x = 0 \end{cases}$ ? (A) $f(x)$ is continuous and differentiable $\forall \text{ x} \in \mathbb{R}$ (B) $f(x)$ is continuous $\forall \text{ x} \in \mathbb{R}$ (C) $f(x)$ is continuous and differentiable $\forall \text{ x} \in \mathbb{R} - \{0\}$ (D) $f(x)$ is discontinuous at infinitely many points