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

Question

5138 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-15T02:01:35

EVEN

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)

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