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

question 92

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