Graphical Behavior

Horizontal Asymptotes

Rule 2

If the degree of the numerator is the same as the degree of the denominator, then the horizontal asymptote has the equation frac1 , where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator.

Example. Determine the horizontal asymptote of the function.

frac2

Both the numerator and denominator are linear, so they have the same degree. The horizontal asymptote is therefore frac3 or y = 2 .

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