Graphing rational functions is a process that involves several steps, starting with finding any existing intercepts, identifying the vertical and horizontal asymptotes, then sketching the graph. As with other methods of graphing, finding intercepts sets the stage for the graph by identifying coordinates that are in turn used to visually display data on the graph. Then, the values of the graph can be determined using a process of division, which continues until X is divided into its smallest factor.
With rational functions, the value of X generally expands. Numbers in the chain of values may be positive or negative, and should increase in value. When numbers begin as negatives, this process involves the values of X moving from negative charges to positive charges. Graphs with rational functions generally contain two intercepts: a y-intercept and an x-intercept. Graphs of rational functions exist as two separate parts, but are connected by the two intercepts. Although they exist on the same plane, the x and y axes never overlap, and are solved separately. Ideally, rational functions reduce to zero, but that only happens when the numerator and denominators do not exist as zero at the same values. The lowest values of X and Y are then plotted on the graph as the vertical asymptote and horizontal asymptote, respectively. These values can then be used to create a rough sketch of the graph.