How do you know if #f(x)= -4x^2 + 4x# is an even or odd function?

1 Answer
Nov 24, 2015

#f(x)# is neither even nor odd.

Explanation:

A function #f(x)# is even if and only if #f(-x) = f(x)#
A function #f(x)# is odd if and only if #f(-x) = -f(x)#

In this case
#f(-x) = -4(-x)^2 + 4(-x) = -4x^2 -4x != f(x)#

and

#-f(x) = -(-4x^2 + 4x) = 4x^2 - 4x != f(-x)#

So
#f(-x) != f(x)#
and
#f(-x) != -f(x)#

meaning #f(x)# is neither even nor odd.