Please explain to me orgin of symmetry, y-axis semmetry, or if its neither.

Question

1. Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.

f(x) = 4x^2 - x^3
-this is how I did it: f(x)=(-4x^2)-x^3,I got this was orgin symmetry

f(x) = 5 - x^4
-f(x)=-x^4 + 5 I got this was y axis symmetry

f(x)=x^3-2x
I got this one to be neither

Answer 1

I am assuming that what you call "origin symmetry" is what is also called an "odd function", for which f(-x) = f(x)
Symmetry such that f(x) = f(-x), about the y axis, is called an even function.

With these definitions,
f(x) = 4x^2 - x^3
has no symmetry
because f(-x) equals neither f(x) nor -f(x), and the last function,
f(x)=x^3-2x has "origin" (odd) symmetry, because f(-x) = -f(x)