Let $f(x) = \begin{cases} |x|+3, & \text{if } x \leq -3 \\ -2x, & \text{if } -3 < x < 3 \\ 6x+2, & \text{if } x \geq 3 \end{cases}$. Determine the continuity of $f(x)$ at $x = -3$ and $x = 3$.
- A$f(x)$ is discontinuous at both $x = -3$ and $x = 3$.
- B$f(x)$ is continuous at $x = -3$ but discontinuous at $x = 3$.
- C$f(x)$ is continuous at $x = -3$ and $x = 3$.
- D$f(x)$ is discontinuous at $x = -3$ but continuous at $x = 3$.
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