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

##### 1 Answer

Oct 18, 2015

Neither

#### Explanation:

The quick way to spot whether a polynomial function in

By definition:

#f(x)# is odd if#f(-x) = -f(x)# for all#x# in the domain.

#f(x)# is even if#f(-x) = f(x)# for all#x# in the domain.

In our case, we find:

#f(-1) = -4-4 = -8#

#f(1) = -4+4 = 0#

So neither condition holds.

Given any function

#f_e(x) = (f(x) + f(-x))/2#

#f_o(x) = (f(x) - f(-x))/2#

In our case we find