 Horizontal line test

For a real-valued function drawn in the plane, the horizontal line test asks whether every horizontal line intersects its function graph at most once. This is exactly injectivity, since two intersections at the same height mean two inputs have the same output. A missing height is compatible with injectivity, so an inverse function is then defined on the image of a function; it is an inverse on the entire specified codomain only when surjectivity also holds.