Solve the Problem $f ( x ) = x ( x - 2 ) ^ { 2 } ( x - 1 )$

Multiple Choice

Solve the problem.
-Which of the following polynomial functions might have the graph shown in the illustration below?

A) $f ( x ) = x ( x - 2 ) ^ { 2 } ( x - 1 )$
B) $f ( x ) = x ^ { 2 } ( x - 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$
C) $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$
D) $f ( x ) = x ( x - 2 ) ( x - 1 ) ^ { 2 }$