When you're looking for vertical asymptotes in the graph of a rational function, you check to see whether or not the denominator has any values of x that could make it zero. I don't have any problems understanding this, or visualizing it.(adsbygoogle = window.adsbygoogle || []).push({});

However, when you check for horizontal or oblique asymptotes, I don't understand the logic of either method. This is the way I've learned to do it...

For a horizontal asymptote [first check to see if the function has one, the denominator must have a greater to or equal order exponent from the numerator] divide by the highest order term and evaluate the limit as x -> infinity.

For an oblique asymptote [first check to see if the fucntion has one, the numerator must be higher order than the denominator] divide the numerator by the denominator and evaluate the lim as x -> infinity.

For horizontal asymptotes, I understand the part about evaluating the limit... the expected value for the limit will be what y approaches but never touches. But I don't understand how the 'check' works or why you divide by the highest order term before evaluating the limit as x-> infinity.

The same goes for oblique asymptotes. I would think that when you just evaluate the rational function for x-> infinity, you would get a linear equation that tells you what y is approaching... again, I don't understand how the check works, or why you divide the numerator by the denominator... can someone explain?

Thanks in advance

Preet

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# Homework Help: Curve Sketching using derivatives

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