Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$$
A) $y$-axis symmetry
B) origin symmetry
C) neither

Question

Quizplus · Accepted Answer

The given polynomial does not exhibit y-axis symmetry because it is not an even function ($f(x) \neq f(-x)$) and it does not exhibit origin symmetry because it is not an odd function ($f(-x) \neq -f(x)$). The presence of both even and odd powers of $x$ without the necessary symmetry in coefficients for y-axis or origin symmetry leads to the conclusion of neither.

Determine Whether the Graph of the Polynomial Has Y-Axis Symmetry f(x)=(x+1)(x−2)(x−1)2f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−2)(x−1)2

Determine Whether the Graph of the Polynomial Has Y-Axis Symmetry $f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$