Which of these describes $f : [-1, 1] \to [-1, 1]$, $f(x) = x\lvert x \rvert$?

Explanation

1. 01

   $f(x) = -x^{2}$ for $x < 0$ and $x^{2}$ for $x \ge 0$: strictly increasing, so one-one.

2. 02

   It runs from $f(-1) = -1$ to $f(1) = 1$: onto $[-1, 1]$.