Methods and apparatus provide mapping functions for video encoding or decoding by replacing a pivot point of a uniformly sampled inverse mapping function by another pivot point not located on an original non-uniformly sampled inverse mapping function. In one embodiment a last pivot point of the inverse mapping function is extended based on a previous slope whose curve is plotted between two previous pivot points or based on the preservation of the slope which is dual to the existing slope of the equivalent section in the forward mapping function. Syntax is provided that assists the mapping and inverse mapping and clipping.