Question

Give an example of a rational function that has a horizontal asymptote of y = 2/9..

Answer 1

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,

$y = \frac{2x - 1}{9x + 2}$


$y = \frac{1 - 6 {x}^{3} }{5x - 27 {x}^{3} }$

Answer 2

The answer to your question to give an example of a rational function that has a horizontal asymptote of y = 2/9 is this one example: f (x) = 2x^2 + 4x + 1  / 9x^2 + x + 1. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.