Oblique Asymptotes appear if the degree of the numerator is exactly one more than the degree of the denominator for which the graph of the rational function will have an oblique asymptote. To find the equation of the oblique asymptote, perform long division by dividing the denominator into the numerator, or do it using synthetic division as long as it works. Finally, the equation of the oblique asymptote will be given when you discard the remainder after the long division. The applet shown below, highlights the oblique or slant asymptote. Try setting the value for the exponent in the leading coefficient of the numerator to 3.
The picture will serve you as guide, since it explains the definition of a rational function.
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