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

Jul 15, 2015

EVEN

#### Explanation:

If it is:
EVEN then: $f \left(- x\right) = f \left(x\right)$
ODD then: $f \left(- x\right) = - f \left(x\right)$

Let us try with:
$x = 2$
$f \left(2\right) = 2 \cdot {2}^{4} + 3 \cdot {2}^{2} = 59$
and:
$x = - 2$
$f \left(- 2\right) = 2 \cdot {\left(- 2\right)}^{4} + 3 \cdot {\left(- 2\right)}^{2} = 59$
so:
$f \left(- 2\right) = f \left(2\right)$ or $f \left(- x\right) = f \left(x\right)$

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)