What statement describes the function f (x) = |x^4-x^3|

You must analyze & graph or sketch this function to answer. The function has 3 roots, x=1, - 3, & 3. This can be found by (x-1) using synthetic division resulting in a remainder of x^2-9 so it factors to:

(x-1) (x+3) (x-3)

This means there are multiple values of X for a given Y, for a portion of the curve, so it is definitely not a 1 on 1 function. It actually passes the vertical line test, but not the horizontal line test so the best answer choice is that it is a many to one fun.