[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given function is an even function, as the polynomial has degree 6, and all the terms in the polynomial has even powers
[tex]{ \qquad \sf \dashrightarrow\:f(-x)=(-x)⁶-2(-x)² + 3} [/tex]
[tex]{ \qquad \sf \dashrightarrow \: f(-x) = x⁶ - 2x² + 3} [/tex]
[tex]{ \qquad \sf \dashrightarrow \: f(-x) = f(x)} [/tex]
As the values for " -x " and " x " are same, since they have even powers.
And if we observe the function properly,
[tex]\qquad \sf \dashrightarrow \: ( {x}^{6} - 2 {x}^{2} ) + 3[/tex]
[ graph of x⁶ - 2x² is symmetric about y - axis, and if we add 3, it shifts 3 units upside so there's no change to symmetry. ]
Conclusion : The graph is symmetric about y - axis.
