Oblique asymptotes
If the degree of the numerator of a rational function is one greater than the degree of the denominator, the graph has an oblique or slant line asymptote. In this interactive figure, you can experiment with the slope and -intercept to try to obtain the oblique asymptote. The graph can be zoomed out to see if the asymptote still looks correct. You can display a divided form of the function (which may not be displayed in its simplified form). Various examples for are given (use the top slider) or you can enter your own example. Changing to another example will reset the axes to their original scale.
Developed for use with Thomas' Calculus, published by Pearson.