Question

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

Answer 1

EVEN...

Explanation:

It's an EVEN function if f(-x) = f(x).

It's an ODD function = f(-x) = -f(x).

(For example, sine is an odd function, cosine is even).

`(-x)^2 * |x| = x^2 * |x|`, since a negative number squared is positive, as is the absolute value of a negative number.

Therefore, this function is EVEN.