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)
$$f ( x ) = \left\{ \begin{array} { l l } | x | , & x \leq 1 \\- ( x - 1 ) ^ { 2 } , & x > 1\end{array} \right.$$