Determine a Piecewise-Defined Function for the Graph Shown Below $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \\ - ( x - 1 ) ^ { 2 } + 1 , & x > 1 \end{array} \right.$

Multiple Choice

Determine a piecewise-defined function for the graph shown below.

A) $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \\ - ( x - 1 ) ^ { 2 } + 1 , & x > 1 \end{array} \right.$
B) $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 0 \\ - ( x - 1 ) ^ { 2 } + 1 , & x \leq 0 \end{array} \right.$
C) $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 1 \\ - x ^ { 2 } , & x \leq 1 \end{array} \right.$
D) $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \geq 0 \\ - x ^ { 2 } , & x \leq 1 \end{array} \right.$
E) $f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \\ - ( x - 1 ) ^ { 2 } , & x > 1 \end{array} \right.$