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kudzordzifrancis
The horizontal asymptote of a rational function tells us the limiting value of that function as it approaches infinity.

For a rational function to have a horizontal asymptote of
[tex] \frac{2}{9} [/tex]
then,[tex]<b>the highest degree of x in the numerator must be equal to the highest degree of x in the denominator.</b>[/tex]

The second condition is that,
[tex]<b>the coefficient of the highest degree in the numerator and the coefficient of the highest degree in the denominator should be in the ratio 2:9.</b>[/tex]

Example are given in the graph above.

Here are some other examples,

[tex] y = \frac{2x - 1}{9x + 2} [/tex]


[tex]y = \frac{1 - 6 {x}^{3} }{5x - 27 {x}^{3} } [/tex]
Ver imagen kudzordzifrancis

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