One-one function

A function $f$ is called one-one function if it never adopts the same value twice.

Geometric proof

A function is one-one if and only if no horizontal line intersects its graph more than once.

In the graph below, the function $y=x^3$ is intersected once by the horizontal line. Therefore the function is geometrically proven to be one-one.

In the graph below, the function $y=x^2$ is intersected twice by the horizontal line. Therefore the function is geometrically proven no to be one-one.