Question

How do you know if `f(x) = 4x^2 + x^4 -120` is an even or odd function?

Answer 1

This function is even, because all the exponents of `x` are even

Explanation:

This is not a general rule, but it is enough for polynomials. If all exponents of `x` are even, then the whole function is even, on the other hand if all exponents are odd, then the whole function is also odd.

For other function the rule is not so simple. We have to calculate `f(-x)`.
If we get `f(-x)=f(x)`, then the function is even,
else if we get: `f(-x)=-f(x)` then the function is odd,
else the function is neither even or odd.

For the given function we get:

`f(-x)=4*(-x)^2+(-x)^4-120`

`f(-x)=4x^2+x^4-120`

`f(-x)=f(x)`

The function is even.