Question

How do you determine if `f(x)= 8x^2` is an even or odd function?

Answer 1

Check `f(-x)` to find that `f(x)=8x^2` is even.

Explanation:

A function `f` is called even if `f(-x) = f(x)` and is called odd if `f(-x) = -f(x)`. Then, to see whether `f` is even or odd, we see how it acts on `-x`.

`f(-x) = 8(-x)^2 = 8x^2 = f(x)`

Thus `f(x)=8x^2` is even.