Question

Is the function `f(x)=2x^4+3x^2` even, odd or neither?

Answer 1

EVEN

Explanation:

If it is:
EVEN then: `f(-x)=f(x)`
ODD then: `f(-x)=-f(x)`

Let us try with:
`x=2`
`f(2)=2*2^4+3*2^2=59`
and:
`x=-2`
`f(-2)=2*(-2)^4+3*(-2)^2=59`
so:
`f(-2)=f(2)` or `f(-x)=f(x)`

Graphically:
graph{2x^4+3x^2 [-16.02, 16.02, -8.01, 8.01]}
(basically the left side is a reflection about the `y` axis of the right side)