Question

How do you determine if `f(x)= x³-x²` is an even or odd function?

Answer 1

It is neither

Explanation:

A function `f(x)` is even if `f(-x)=f(x)`, and it is odd if `f(-x) = -f(x)`.

For the given function `f(x) =x^3-x^2`, we have

`f(-x) = (-x)^3-(-x)^2 = (-1)^3x^3-(-1)^2x^2=-x^3-x^2`

this is neither `f(x)`, nor `-f(x)` (which is `-x^3+x^2`.

Note that a polynomial is even if it only consists of even powers of `x`, and odd if it only consists of odd powers (hence the name) - the given function contains both kinds!