Question

Consider the function f(x)=4x^2-3x^4.

Is the function even, odd, or neither?

Evaluate the function at the given values of the independent variable and simplify. f(-3), f(-x)

Answer 1

A function is odd if f(x) = -f(-x)
A function is even if ....

Check whether or not the function you've written down satisfies either definition.

Answer 2

f(-x) = -f(x) means odd
f(-x) = f(x) means even
the function is even.
f(-3) = 4 * (-3)^2 - 3 * (-3)^4 = -207
f(-x) = 4 * (-x)^2 - 3*(-x)^4 -> 4x^2 -3x^4
which is not surprising since the function is even :)