I.

For any function f, f is continuous at x = c if and only if $$\lim_{x\to c} f(x)$$ exists and equals $$f(c)$$.

II.

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

III.

For the given function, $$f(2)=3*2^2=12$$.

Based on the definitions of continuity and the provided function, which of the above statements are true?