Inside Collection (Course): "Rational"ity

Summary: Finding horizontal asymptotes of rational functions

Horizontal asymptotes are horizontal lines the graph approaches.

Horizontal Asymptotes CAN be crossed.

To find horizontal asymptotes:

- If the degree (the largest exponent) of the denominator is
*bigger than*the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). - If the degree of the numerator is
*bigger than*the denominator, there is no horizontal asymptote. - If the degrees of the numerator and denominator are the
*same*, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

- BOBO - Bigger on bottom, y=0
- BOTN - Bigger on top, none
- EATS DC - Exponents are the same, divide coefficients

Find the Horizontal Asymptotes of the following:

None since the degree of the numerator is greater than the degree of the denominator.

y = 0

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