Continuity of a Piecewise Function

I. A function f is continuous at x = c if and only if $\lim_{x\to c} f(x)$ exists and is equal to $f(c)$.

II. For the function $f(x)=\begin{cases}3x^2 & \text{if } x \le 2 \\ 6x-6 & \text{if } x > 2\end{cases}$, f is continuous at x = 2 if its left-hand limit at 2 differs from $f(2)$.

III. For the function defined in statement II, $f(2) = 3(2^2) = 12$.

Which of the above statements are true?