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

1 Answer
Jul 15, 2015

Answer:

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)