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
\(\frac{2}{9}\)
then,\(the highest degree of x in the numerator must be equal to the highest degree of x in the denominator.\)
The second condition is that,
\(the coefficient of the highest degree in the numerator and the coefficient of the highest degree in the denominator should be in the ratio 2:9.\)
Example are given in the graph above.
Here are some other examples,
\(y = \frac{2x - 1}{9x + 2}\)
\(y = \frac{1 - 6 {x}^{3} }{5x - 27 {x}^{3} }\)
