Given a real-coefficient cubic polynomial function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + 3$ . Let $g ( x ) = f ( - x ) - 3$ . It is known that the graph of $y = g ( x )$ has a center of symmetry at $( 1,0 )$ and $g ( - 1 ) < 0$ . Select the correct options. (1) $g ( x ) = 0$ has three distinct integer roots (2) $a < 0$ (3) The center of symmetry of the graph of $y = f ( x )$ is $( - 1 , - 3 )$ (4) $f ( 100 ) < 0$ (5) The graph of $y = f ( x )$ near the point $( - 1 , f ( - 1 ) )$ can be approximated by a line with slope $a$
Given a real-coefficient cubic polynomial function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + 3$ . Let $g ( x ) = f ( - x ) - 3$ . It is known that the graph of $y = g ( x )$ has a center of symmetry at $( 1,0 )$ and $g ( - 1 ) < 0$ . Select the correct options.\\
(1) $g ( x ) = 0$ has three distinct integer roots\\
(2) $a < 0$\\
(3) The center of symmetry of the graph of $y = f ( x )$ is $( - 1 , - 3 )$\\
(4) $f ( 100 ) < 0$\\
(5) The graph of $y = f ( x )$ near the point $( - 1 , f ( - 1 ) )$ can be approximated by a line with slope $a$