AlgebraPolynomails
posted by Sam on .
Please explain to me orgin of symmetry, yaxis semmetry, or if its neither.
1. Determine whether the graph of the polynomial has yaxis 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^32x
I got this one to be neither

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^32x has "origin" (odd) symmetry, because f(x) = f(x)