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

Solution:

We know that

An oblique asymptote y = kx + b of graph of function where y = f(x)

\(\\k=\lim_{x\rightarrow +\varpi }\frac{f(x)}{x} \\ \\b=\lim_{x\rightarrow +\varpi }[f(x)-kx]\)

In the similar way, x will be same as x → -∞

Assume a function y = (2x + 4)/ (9x + 5)

Here horizontal asymptote y = kx + b

k = 0 and b = 2/9

So y = 2/9

So the assumed function is correct which has horizontal asymptote y = 2/9.

Therefore, an example of a rational function is y = (2x + 4)/(9x + 5).

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

Summary:

An example of a rational function that has a horizontal asymptote of y = 2/9 is y = (2x + 4)/ (9x + 5).