Question

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

Answer 1

we know, an oblique asymptote y = kx + b of graph of the function y = f(x)
where $k=\displaystyle\lim_{x\to+\infty}\frac{f(x)}{x}$

$b=\displaystyle\lim_{x\to+\infty}(f(x)-kx)$
in similar way we define the limits will be same as $x\to-\infty$

Now , Let any function $y=\frac{2x+4}{9x+5}$
here, Let horizontal asymptote y = kx + b
now, k = 0 and b = 2/9
e.g., y = 2/9
hence, the function we assumed is correct which has horizontal asymptote y = 2/9 . you can better understand by figure and I attached the figure of function and asymptote .