Limits of graphic display design component variation based on cognitive tolerance for imprecision were investigated using compatibility functions. The compatibility function is an empirical definition of a perceptual category representing the grade of membership of an implied physical attribute into a corresponding conceptual category, measuring the degree of compatibility between a particular level of attribute and a category. Adults (N=24) were asked to categorize lines as sharply or slightly increasing when presented with line and bar graphs with slopes from five to sixty degrees in five degree increments. Crossover point and precision parameters are discussed as part of the statistical analysis. This experiment established compatibility function values for the categorical terms sharply increasing and slightly increasing. A graph designer having an inventory of such functions plus the operations that can be performed on them can weight the information to be presented by manipulating various aspects of the graph, specifically the framework and/or specifier. This would allow graphs to be designed to meet specialized requirements. A list of twelve references, figures showing the types of graphs used, and the compatibility functions established fo the categories of interest to this experiment; and a table summarizing parameter values for the mathematical models are attached. (JM)