Find the Rule That Defines Each Piecewise-Defined Function $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$

Find the rule that defines each piecewise-defined function.
-

A) $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$
B) $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.$
C) $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x + \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$
D) $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$