Which one of the following functions is continuous at x = 3?

A. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {2,}&{{\text{if}}}&{{\text{x}} = 3} \\ {{\text{x}} - 1,}&{{\text{if}}}&{{\text{x}} > 3} \\ {\frac{{{\text{x}} + 3}}{3},}&{{\text{if}}}&{{\text{x}} < 3} \end{array}} \right.\]

B. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {4,}&{{\text{if}}}&{{\text{x}} = 3} \\ {8 - {\text{x,}}}&{{\text{if}}}&{{\text{x}} \ne 3} \end{array}} \right.\]

C. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{\text{x}} + 3,}&{{\text{if}}}&{{\text{x}} \leqslant 3} \\ {{\text{x}} - 4,}&{{\text{if}}}&{{\text{x}} > 3} \end{array}} \right.\]

D. $${\text{f}}\left( {\text{x}} \right) = \frac{1}{{{{\text{x}}^3} - 27}},\,{\text{if}}\,{\text{x}} \ne 3$$

Answer: Option A