Question

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

Answer 1

Note that the graph of the function
`\displaystyle{ f(x)= (1)/(x)` has 2 asymptotes:

The horizontal asymptote x=0,

and the vertical asymptote y=0, as shown in the first picture.


Adding 2/9 to this function, creating
`\displaystyle{ g(x)= (1)/(x)+(2)/(9)`, shifts the first graph 2/9 units up. It also shifts the horizontal asymptote y=0 to t=2/9.

We can express the function as
`\displaystyle{ (1)/(x)+ (2)/(9)= (9)/(9x)+ (2x)/(9x)= (2x+9)/(9x)`.


Answer:
`\displaystyle{ (2x+9)/(9x)`