Question

How do you know if `f(x)=x^4-6^-4+3x^2` is an even or odd function?

Answer 1

If it is even , then `f(-x)=f(x)`

If it is odd , then `f(-x)=-f(x)`

Explanation:

`f(-x)=(-x)^4-6^-4+3(-x)^2=x^4-6^-4+3x^2=f(x)`

So, it is even and notice the symmetry with respect to the y-axis (graph below).

Hope that helped