Limit Analysis of Rational Function

Let the function $$ f $$ be defined by:

$$ f(x) =\frac{3x^2 - 12}{x - 2} $$

Determine the value of the limit of the function as $$ x $$ approaches 2 by evaluating the following:

1. Identify the behavior of $$ f(x) $$ as $$ x $$ approaches 2 from the left (denoted as $$ f(2^-) $$).
2. Identify the behavior of $$ f(x) $$ as $$ x $$ approaches 2 from the right (denoted as $$ f(2^+) $$).

Based on your findings, compare the two quantities: